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Journal articles on the topic 'Moduli space'

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Published: 4 June 2021
Last updated: 8 June 2024

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1

Chai, Ching-Li. "moduli space." Duke Mathematical Journal 82, no. 3 (March 1996): 725–54. http://dx.doi.org/10.1215/s0012-7094-96-08230-7.

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2

Manolache, Cristina. "Stable maps and stable quotients." Compositio Mathematica 150, no. 9 (July 17, 2014): 1457–81. http://dx.doi.org/10.1112/s0010437x14007258.

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AbstractWe analyze the relationship between two compactifications of the moduli space of maps from curves to a Grassmannian: the Kontsevich moduli space of stable maps and the Marian–Oprea–Pandharipande moduli space of stable quotients. We construct a moduli space which dominates both the moduli space of stable maps to a Grassmannian and the moduli space of stable quotients, and equip our moduli space with a virtual fundamental class. We relate the virtual fundamental classes of all three moduli spaces using the virtual push-forward formula. This gives a new proof of a theorem of Marian–Oprea–Pandharipande: that enumerative invariants defined as intersection numbers in the stable quotient moduli space coincide with Gromov–Witten invariants.
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3

Frühbis-Krüger, Anne. "Computing moduli spaces for space curve singularities." Journal of Pure and Applied Algebra 164, no. 1-2 (October 2001): 165–78. http://dx.doi.org/10.1016/s0022-4049(00)00152-3.

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4

Sato, Matsuo. "Moduli Space in Homological Mirror Symmetry." Advances in Mathematical Physics 2019 (April 30, 2019): 1–11. http://dx.doi.org/10.1155/2019/1693102.

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We prove that the moduli space of the pseudo holomorphic curves in the A-model on a symplectic torus is homeomorphic to a moduli space of Feynman diagrams in the configuration space of the morphisms in the B-model on the corresponding elliptic curve. These moduli spaces determine the A∞ structure of the both models.
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5

Farkas, Gavril, and Rahul Pandharipande. "THE MODULI SPACE OF TWISTED CANONICAL DIVISORS." Journal of the Institute of Mathematics of Jussieu 17, no. 3 (April 5, 2016): 615–72. http://dx.doi.org/10.1017/s1474748016000128.

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The moduli space of canonical divisors (with prescribed zeros and poles) on nonsingular curves is not compact since the curve may degenerate. We define a proper moduli space of twisted canonical divisors in $\overline{{\mathcal{M}}}_{g,n}$ which includes the space of canonical divisors as an open subset. The theory leads to geometric/combinatorial constraints on the closures of the moduli spaces of canonical divisors.In case the differentials have at least one pole (the strictly meromorphic case), the moduli spaces of twisted canonical divisors on genus $g$ curves are of pure codimension $g$ in $\overline{{\mathcal{M}}}_{g,n}$. In addition to the closure of the canonical divisors on nonsingular curves, the moduli spaces have virtual components. In the Appendix A, a complete proposal relating the sum of the fundamental classes of all components (with intrinsic multiplicities) to a formula of Pixton is proposed. The result is a precise and explicit conjecture in the tautological ring for the weighted fundamental class of the moduli spaces of twisted canonical divisors.As a consequence of the conjecture, the classes of the closures of the moduli spaces of canonical divisors on nonsingular curves are determined (both in the holomorphic and meromorphic cases).
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6

Diez, Tobias, and Gerd Rudolph. "Normal form of equivariant maps in infinite dimensions." Annals of Global Analysis and Geometry 61, no. 1 (October 14, 2021): 159–213. http://dx.doi.org/10.1007/s10455-021-09777-2.

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AbstractLocal normal form theorems for smooth equivariant maps between infinite-dimensional manifolds are established. These normal form results are new even in finite dimensions. The proof is inspired by the Lyapunov–Schmidt reduction for dynamical systems and by the Kuranishi method for moduli spaces. It uses a slice theorem for Fréchet manifolds as the main technical tool. As a consequence, the abstract moduli space obtained by factorizing a level set of the equivariant map with respect to the group action carries the structure of a Kuranishi space, i.e., such moduli spaces are locally modeled on the quotient by a compact group of the zero set of a smooth map. The general results are applied to the moduli space of anti-self-dual instantons, the Seiberg–Witten moduli space and the moduli space of pseudoholomorphic curves.
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7

RADNELL, DAVID, and ERIC SCHIPPERS. "QUASISYMMETRIC SEWING IN RIGGED TEICHMÜLLER SPACE." Communications in Contemporary Mathematics 08, no. 04 (August 2006): 481–534. http://dx.doi.org/10.1142/s0219199706002210.

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One of the basic geometric objects in conformal field theory (CFT) is the moduli space of Riemann surfaces whose n boundaries are "rigged" with analytic parametrizations. The fundamental operation is the sewing of such surfaces using the parametrizations to identify points. An alternative model is the moduli space of n-punctured Riemann surfaces together with local biholomorphic coordinates at the punctures. We refer to both of these moduli spaces as the "rigged Riemann moduli space".By generalizing to quasisymmetric boundary parametrizations, and defining rigged Teichmüller spaces in both the border and puncture pictures, we prove the following results: (1) The Teichmüller space of a genus-g surface bordered by n closed curves covers the rigged Riemann and rigged Teichmüller moduli spaces of surfaces of the same type, and induces complex manifold structures on them; (2) With this complex structure, the sewing operation is holomorphic; (3) The border and puncture pictures of the rigged moduli and rigged Teichmüller spaces are biholomorphically equivalent.These results are necessary in rigorously defining CFT (in the sense of G. Segal), as well as for the construction of CFT from vertex operator algebras.
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8

MUKAI-HIDANO, MARIKO, and YOSHIHIRO OHNITA. "GEOMETRY OF THE MODULI SPACES OF HARMONIC MAPS INTO LIE GROUPS VIA GAUGE THEORY OVER RIEMANN SURFACES." International Journal of Mathematics 12, no. 03 (May 2001): 339–71. http://dx.doi.org/10.1142/s0129167x01000733.

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This paper aims to investigate the geometry of the moduli spaces of harmonic maps of compact Riemann surfaces into compact Lie groups or compact symmetric spaces. The approach here is to study the gauge theoretic equations for such harmonic maps and the moduli space of their solutions. We discuss the S1-action, the hyper-presymplectic structure, the energy function, the Hitchin map, the flag transforms on the moduli space, several kinds of subspaces in the moduli space, and the relationship among them, especially the structure of the critical point subset for the energy function on the moduli space. As results, we show that every uniton solution is a critical point of the energy function on the moduli space, and moreover we give a characterization of the fixed point subset fixed by S1-action in terms of a flag transform.
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9

BARRON, KATRINA. "THE MODULI SPACE OF N = 2 SUPER-RIEMANN SPHERES WITH TUBES." Communications in Contemporary Mathematics 09, no. 06 (December 2007): 857–940. http://dx.doi.org/10.1142/s0219199707002666.

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Within the framework of complex supergeometry and motivated by two-dimensional genus-zero holomorphic N = 2 superconformal field theory, we define the moduli space of N = 2 super-Riemann spheres with oriented and ordered half-infinite tubes (or equivalently, oriented and ordered punctures, and local superconformal coordinates vanishing at the punctures), modulo N = 2 superconformal equivalence. We develop a formal theory of infinitesimal N = 2 superconformal transformations based on a representation of the N = 2 Neveu–Schwarz algebra in terms of superderivations. In particular, via these infinitesimals we present the Lie supergroup of N = 2 superprojective transformations of the N = 2 super-Riemann sphere. We give a reformulation of the moduli space in terms of these infinitesimals. We introduce generalized N = 2 super-Riemann spheres with tubes and discuss some group structures associated to certain moduli spaces of both generalized and non-generalized N = 2 super-Riemann spheres. We define an action of the symmetric groups on the moduli space. Lastly we discuss the nonhomogeneous (versus homogeneous) coordinate system associated to N = 2 superconformal structures and the corresponding results in this coordinate system.
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10

Fialowski, Alice, and Michael Penkava. "Moduli spaces of low-dimensional Lie superalgebras." International Journal of Mathematics 32, no. 09 (July 3, 2021): 2150059. http://dx.doi.org/10.1142/s0129167x21500592.

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In this paper, we study moduli spaces of low-dimensional complex Lie superalgebras. We discover a similar pattern for the structure of these moduli spaces as we observed for ordinary Lie algebras, namely, that there is a stratification of the moduli space by projective orbifolds. The moduli spaces consist of some families as well as some singleton elements. The different strata are linked by jump deformations, which gives a unique manner of decomposing the moduli space which is consistent with deformation theory.
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11

Greb, Daniel, Julius Ross, and Matei Toma. "Moduli of vector bundles on higher-dimensional base manifolds — Construction and variation." International Journal of Mathematics 27, no. 07 (June 2016): 1650054. http://dx.doi.org/10.1142/s0129167x16500543.

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We survey recent progress in the study of moduli of vector bundles on higher-dimensional base manifolds. In particular, we discuss an algebro-geometric construction of an analogue for the Donaldson–Uhlenbeck compactification and explain how to use moduli spaces of quiver representations to show that Gieseker–Maruyama moduli spaces with respect to two different chosen polarizations are related via Thaddeus-flips through other “multi-Gieseker”-moduli spaces of sheaves. Moreover, as a new result, we show the existence of a natural morphism from a multi-Gieseker moduli space to the corresponding Donaldson–Uhlenbeck moduli space.
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12

Krusch, Steffen, and Abera A. Muhamed. "Moduli spaces of lumps on real projective space." Journal of Mathematical Physics 56, no. 8 (August 2015): 082901. http://dx.doi.org/10.1063/1.4928925.

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13

Khalfallah, Adel. "The moduli space of hyperbolic compact complex spaces." Mathematische Zeitschrift 255, no. 4 (August 26, 2006): 691–702. http://dx.doi.org/10.1007/s00209-006-0036-9.

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14

DOMOKOS, MÁTYÁS. "ON SINGULARITIES OF QUIVER MODULI." Glasgow Mathematical Journal 53, no. 1 (August 25, 2010): 131–39. http://dx.doi.org/10.1017/s0017089510000583.

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AbstractAny moduli space of representations of a quiver (possibly with oriented cycles) has an embedding as a dense open subvariety into a moduli space of representations of a bipartite quiver having the same type of singularities. A connected quiver is Dynkin or extended Dynkin if and only if all moduli spaces of its representations are smooth.
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15

MACHU, FRANCOIS-XAVIER. "LOCAL STRUCTURE OF MODULI SPACES." International Journal of Mathematics 22, no. 12 (December 2011): 1683–709. http://dx.doi.org/10.1142/s0129167x11007409.

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We provide a sketch of the GIT construction of the moduli spaces for the three classes of connections: the class of meromorphic connections with fixed divisor of poles D and its subclasses of integrable and integrable logarithmic connections. We use the Luna Slice Theorem to represent the germ of the moduli space as the quotient of the Kuranishi space by the automorphism group of the central fiber. This method is used to determine the singularities of the moduli space of connections in some examples.
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16

ISIDRO, JOSÉ M. "MODULI OF QUANTA." International Journal of Geometric Methods in Modern Physics 03, no. 02 (March 2006): 177–86. http://dx.doi.org/10.1142/s0219887806001089.

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The classical phase of the matrix model of 11-dimensional M-theory is complex, infinite-dimensional Hilbert space. As a complex manifold, the latter admits a continuum of nonequivalent, complex-differentiable structures that can be placed in 1-to-1 correspondence with families of coherent states in the Hilbert space of quantum states. The moduli space of nonbiholomorphic complex structures on classical phase space turns out to be an infinite-dimensional symmetric space. We argue that each choice of a complex differentiable structure gives rise to a physically different notion of an elementary quantum.
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17

Maican, Mario. "Moduli of stable sheaves supported on curves of genus three contained in a quadric surface." Advances in Geometry 20, no. 4 (October 27, 2020): 507–22. http://dx.doi.org/10.1515/advgeom-2019-0025.

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AbstractWe study the moduli space of stable sheaves of Euler characteristic 1 supported on curves of arithmetic genus 3 contained in a smooth quadric surface. We show that this moduli space is rational. We compute its Betti numbers by studying the variation of the moduli spaces of α-semi-stable pairs. We classify the stable sheaves using locally free resolutions or extensions. We give a global description: the moduli space is obtained from a certain flag Hilbert scheme by performing two flips followed by a blow-down.
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18

Baker, Matthew, and Oliver Lorscheid. "The moduli space of matroids." Advances in Mathematics 390 (October 2021): 107883. http://dx.doi.org/10.1016/j.aim.2021.107883.

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19

Landsteiner, Karl, John M. Pierre, and Steven B. Giddings. "Moduli space ofN=2supersymmetricG2gauge theory." Physical Review D 55, no. 4 (February 15, 1997): 2367–72. http://dx.doi.org/10.1103/physrevd.55.2367.

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20

Aouina, Mokhtar. "The moduli space of thickenings." Transactions of the American Mathematical Society 364, no. 12 (December 1, 2012): 6689–717. http://dx.doi.org/10.1090/s0002-9947-2012-05645-5.

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21

Bak, Dongsu, Yoshifumi Hyakutake, and Nobuyoshi Ohta. "Phase moduli space of supertubes." Nuclear Physics B 696, no. 1-2 (September 2004): 251–62. http://dx.doi.org/10.1016/j.nuclphysb.2004.07.010.

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22

Becker, Melanie, Li-Sheng Tseng, and Shing-Tung Yau. "Moduli space of torsional manifolds." Nuclear Physics B 786, no. 1-2 (December 2007): 119–34. http://dx.doi.org/10.1016/j.nuclphysb.2007.07.006.

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23

Giorgadze, G. "Moduli space of complex structures." Journal of Mathematical Sciences 160, no. 6 (July 22, 2009): 697–716. http://dx.doi.org/10.1007/s10958-009-9522-z.

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24

Maskit, Bernard. "A picture of moduli space." Inventiones Mathematicae 126, no. 2 (October 2, 1996): 341–90. http://dx.doi.org/10.1007/s002220050103.

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25

Myers, Robert C., and Vipul Periwal. "Topological gravity and moduli space." Nuclear Physics B 333, no. 2 (March 1990): 536–50. http://dx.doi.org/10.1016/0550-3213(90)90050-n.

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26

Barnard, Roger W., and G. Brock Williams. "Combinatorial excursions in moduli space." Pacific Journal of Mathematics 205, no. 1 (July 1, 2002): 3–30. http://dx.doi.org/10.2140/pjm.2002.205.3.

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27

Liu, Kefeng. "Heat Kernel and Moduli Space." Mathematical Research Letters 3, no. 6 (1996): 743–62. http://dx.doi.org/10.4310/mrl.1996.v3.n6.a3.

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28

Buff, Xavier, Adam L. Epstein, and Sarah Koch. "Prefixed curves in moduli space." American Journal of Mathematics 144, no. 6 (December 2022): 1485–509. http://dx.doi.org/10.1353/ajm.2022.0036.

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29

Dubrovskiy, Stanislav. "Moduli Space of Fedosov Structures." Annals of Global Analysis and Geometry 27, no. 3 (May 2005): 273–97. http://dx.doi.org/10.1007/s10455-005-1585-6.

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30

Dubrovskiy, S. "Moduli space of symmetric connections." Journal of Mathematical Sciences 126, no. 2 (January 2005): 1053–63. http://dx.doi.org/10.1007/pl00021951.

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31

Bhosle, Usha N. "Hitchin pairs on reducible curves." International Journal of Mathematics 29, no. 03 (March 2018): 1850015. http://dx.doi.org/10.1142/s0129167x18500155.

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We define semistable generalized parabolic Hitchin pairs (GPH) on a disjoint union [Formula: see text] of integral smooth curves and construct their moduli spaces. We define a Hitchin map on the moduli space of GPH and show that it is a proper map. We construct moduli spaces of semistable Hitchin pairs on a reducible projective curve [Formula: see text]. When [Formula: see text] is the normalization of [Formula: see text], we give a birational morphism [Formula: see text] from the moduli space [Formula: see text] of good GPH on [Formula: see text] to the moduli space [Formula: see text] of Hitchin pairs on [Formula: see text] and show that the Hitchin map on [Formula: see text] induces a proper Hitchin map on [Formula: see text]. We determine the fibers of the Hitchin maps. We study the relationship between representations of the (topological) fundamental group of [Formula: see text] and Higgs bundles on [Formula: see text]. We show that if all the irreducible components of [Formula: see text] are smooth, then the Hitchin map is defined on the entire moduli space [Formula: see text].
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32

Hu, Guangming, Hideki Miyachi, and Yi Qi. "Universal commensurability augmented Teichmüller space and moduli space." Annales Fennici Mathematici 46, no. 2 (2021): 897–907. http://dx.doi.org/10.5186/aasfm.2021.4660.

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33

MA, LI. "Moduli space of special Lagrangians in almost Kahler spaces." Anais da Academia Brasileira de Ciências 73, no. 1 (March 2001): 01–05. http://dx.doi.org/10.1590/s0001-37652001000100001.

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34

Cherkis, Sergey A. "Moduli Spaces of Instantons on the Taub-NUT Space." Communications in Mathematical Physics 290, no. 2 (June 26, 2009): 719–36. http://dx.doi.org/10.1007/s00220-009-0863-8.

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35

SABRA, W. A., S. THOMAS, and N. VANEGAS. "SPECIAL GEOMETRY AND TWISTED MODULI IN ORBIFOLD THEORIES WITH CONTINUOUS WILSON LINES." Modern Physics Letters A 11, no. 16 (May 30, 1996): 1307–16. http://dx.doi.org/10.1142/s0217732396001314.

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Target space duality symmetries, which acts on Kähler and continuous Wilson line moduli, of a ZN (N≠2) two-dimensional subspace of the moduli space of orbifold compactification are modified to include twisted moduli. These spaces described by the cosets [Formula: see text] are special Kähler, a fact which is exploited in deriving the extension of tree level duality transformation to include higher orders of the twisted moduli. Also, restrictions on these higher order terms are derived.
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36

Iena, Oleksandr. "On the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics." Open Mathematics 16, no. 1 (February 23, 2018): 46–62. http://dx.doi.org/10.1515/math-2018-0003.

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AbstractA parametrization of the fine Simpson moduli spaces of 1-dimensional sheaves supported on plane quartics is given: we describe the gluing of the Brill-Noether loci described by Drézet and Maican, provide a common parameter space for these loci, and show that the Simpson moduli space M = M4m ± 1(ℙ2) is a blow-down of a blow-up of a projective bundle over a smooth moduli space of Kronecker modules. Two different proofs of this statement are given.
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37

La Nave, Gabriele, and Chih-Chung Liu. "The Gromov limit for vortex moduli spaces." Reviews in Mathematical Physics 31, no. 02 (February 27, 2019): 1950004. http://dx.doi.org/10.1142/s0129055x19500041.

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We generalize the descriptions of vortex moduli spaces in [4] to more than one section with adiabatic constant [Formula: see text]. The moduli space is topologically independent of [Formula: see text] but is not compact with respect to [Formula: see text] topology. Following [17], we construct a Gromov limit for vortices of fixed energy, and attempt to compactify the moduli space via bubble trees with possibly conical bubbles (or raindrops).
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38

HAUZER, MARCIN, and ADRIAN LANGER. "MODULI SPACES OF FRAMED PERVERSE INSTANTONS ON ℙ3." Glasgow Mathematical Journal 53, no. 1 (August 25, 2010): 51–96. http://dx.doi.org/10.1017/s0017089510000558.

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AbstractWe study moduli spaces of framed perverse instantons on ℙ3. As an open subset, it contains the (set-theoretical) moduli space of framed instantons studied by I. Frenkel and M. Jardim in [9]. We also construct a few counter-examples to earlier conjectures and results concerning these moduli spaces.
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39

Alper, Jarod, Maksym Fedorchuk, and David Ishii Smyth. "Second flip in the Hassett–Keel program: existence of good moduli spaces." Compositio Mathematica 153, no. 8 (May 15, 2017): 1584–609. http://dx.doi.org/10.1112/s0010437x16008289.

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We prove a general criterion for an algebraic stack to admit a good moduli space. This result may be considered as a generalization of the Keel–Mori theorem, which guarantees the existence of a coarse moduli space for a separated Deligne–Mumford stack. We apply this result to prove that the moduli stacks $\overline{{\mathcal{M}}}_{g,n}(\unicode[STIX]{x1D6FC})$ parameterizing $\unicode[STIX]{x1D6FC}$-stable curves introduced in [J. Alper et al., Second flip in the Hassett–Keel program: a local description, Compositio Math. 153 (2017), 1547–1583] admit good moduli spaces.
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40

CASTRAVET, ANA-MARIA. "RATIONAL FAMILIES OF VECTOR BUNDLES ON CURVES." International Journal of Mathematics 15, no. 01 (February 2004): 13–45. http://dx.doi.org/10.1142/s0129167x0400220x.

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Let C be a smooth projective complex curve of genus g≥2 and let M be the moduli space of rank 2, stable vector bundles on C, with fixed determinant of degree 1. For any k≥1, we find all the irreducible components of the space of rational curves on M, of degree k. In particular, we find the maximal rationally connected fibrations of these components. We prove that there is a one-to-one correspondence between moduli spaces of rational curves on M and moduli spaces of rank 2 vector bundles on ℙ1×C.
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41

Deng, Jialong. "Metric topology on the moduli space." Applied General Topology 22, no. 1 (April 1, 2021): 11. http://dx.doi.org/10.4995/agt.2021.13066.

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<p>We define the smooth Lipschitz topology on the moduli space and show that each conformal class is dense in the moduli space endowed with Gromov-Hausdorff topology, which offers an answer to Tuschmann’s question.</p>
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42

Inaba, Michi-Aki. "On the moduli of stable sheaves on a reducible projective scheme and examples on a reducible quadric surface." Nagoya Mathematical Journal 166 (June 2002): 135–81. http://dx.doi.org/10.1017/s0027763000008291.

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AbstractWe study the moduli space of stable sheaves on a reducible projective scheme by use of a suitable stratification of the moduli space. Each stratum is the moduli space of “triples”, which is the main object investigated in this paper. As an application, we can see that the relative moduli space of rank two stable sheaves on quadric surfaces gives a nontrivial example of the relative moduli space which is not flat over the base space.
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43

Kapovich, Michael, and John J. Millson. "On the Moduli Space of a Spherical Polygonal Linkage." Canadian Mathematical Bulletin 42, no. 3 (September 1, 1999): 307–20. http://dx.doi.org/10.4153/cmb-1999-037-x.

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AbstractWe give a “wall-crossing” formula for computing the topology of the moduli space of a closed n-gon linkage on 𝕊2. We do this by determining the Morse theory of the function ρn on the moduli space of n-gon linkages which is given by the length of the last side—the length of the last side is allowed to vary, the first (n − 1) side-lengths are fixed. We obtain a Morse function on the (n − 2)-torus with level sets moduli spaces of n-gon linkages. The critical points of ρn are the linkages which are contained in a great circle. We give a formula for the signature of the Hessian of ρn at such a linkage in terms of the number of back-tracks and the winding number. We use our formula to determine the moduli spaces of all regular pentagonal spherical linkages.
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44

Kwun, Young Chel, Hussain Minhaj Uddin Ahmad Qadri, Waqas Nazeer, Absar Ul Haq, and Shin Min Kang. "On Generalized Moduli of Quasi-Banach Space." Journal of Function Spaces 2018 (2018): 1–10. http://dx.doi.org/10.1155/2018/7324783.

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We shall discuss three generalized moduli such as generalized modulus of convexity, modulus of smoothness, and modulus of Zou-Cui of quasi-Banach spaces and give some important properties of these moduli. Furthermore, we establish relationships of these generalized moduli with each other.
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45

Gotou, Rin. "Dynamical systems of correspondences on the projective line I: Moduli spaces and multiplier maps." Conformal Geometry and Dynamics of the American Mathematical Society 27, no. 8 (July 26, 2023): 294–321. http://dx.doi.org/10.1090/ecgd/387.

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We consider moduli spaces of dynamical systems of correspondences over the projective line as a generalization of moduli spaces of dynamical systems of endomorphisms on the projective line. We define the moduli space D y n d , e Dyn_{d,e} of degree ( d , e ) (d,e) correspondences. We construct a family ρ c : D y n d , e ⇢ D y n 1 , d + e − 1 \rho _c : Dyn_{d,e} \dashrightarrow Dyn_{1,d+e-1} of rational maps representation-theoretically. Here we note that D y n 1 , d + e − 1 Dyn_{1,d+e-1} is identical to the moduli space of the usual dynamical systems of degree d + e − 1 d+e-1 . We show that the moduli space D y n d , e Dyn_{d,e} is rational by using ρ c \rho _c . Moreover, the multiplier maps for the fixed points factor through ρ c \rho _c . Furthermore, we show the Woods Hole formulae for correspondences of different degrees are also related by ρ c \rho _c and obtain another representation-theoretically simplified form of the formula.
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46

Teleman, Andrei. "Analytic cycles in flip passages and in instanton moduli spaces over non-Kählerian surfaces." International Journal of Mathematics 27, no. 07 (June 2016): 1640009. http://dx.doi.org/10.1142/s0129167x16400097.

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Let [Formula: see text] ([Formula: see text]) be a moduli space of stable (polystable) bundles with fixed determinant on a complex surface with [Formula: see text] and let [Formula: see text] be a pure [Formula: see text]-dimensional analytic set. We prove a general formula for the homological boundary [Formula: see text] of the Borel–Moore fundamental class of [Formula: see text] in the boundary of the blown up moduli space [Formula: see text]. The proof is based on the holomorphic model theorem of [A. Teleman, Instanton moduli spaces on non-Kählerian surfaces, Holomorphic models around the reduction loci, J. Geom. Phys. 91 (2015) 66–87] which identifies a neighborhood of a boundary component of [Formula: see text] with a neighborhood of the boundary of a “blown up flip passage”. We then focus on a particular instanton moduli space which intervenes in our program for proving the existence of curves on class VII surfaces. Using our result, combined with general properties of the Donaldson cohomology classes, we prove incidence relations between the Zariski closures (in the considered moduli space) of certain families of extensions. These incidence relations are crucial for understanding the geometry of the moduli space, and cannot be obtained using classical complex geometric deformation theory.
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47

SODA, JIRO, and YUKI YAMANAKA. "MODULI SPACE OF CHERN-SIMONS GRAVITY." Modern Physics Letters A 06, no. 04 (February 10, 1991): 303–12. http://dx.doi.org/10.1142/s0217732391000270.

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Conformally invariant (2+1)-dimensional gravity, Chern-Simons gravity, is studied. Its solution space, moduli space, is investigated using the linearization method. The dimension of moduli space is determined as 18g–18 for g>1, 6 for g=1 and 0 for g=0. We discuss the geometrical meaning of our investigation.
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48

McMullen, Curtis. "Navigating moduli space with complex twists." Journal of the European Mathematical Society 15, no. 4 (2013): 1223–43. http://dx.doi.org/10.4171/jems/390.

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49

Eskin, Alex, and Maryam Mirzakhani. "Counting closed geodesics in moduli space." Journal of Modern Dynamics 5, no. 1 (2011): 71–105. http://dx.doi.org/10.3934/jmd.2011.5.71.

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50

Cruz-Cota, Aldo-Hilario. "The moduli space of hex spheres." Algebraic & Geometric Topology 11, no. 3 (May 11, 2011): 1323–43. http://dx.doi.org/10.2140/agt.2011.11.1323.

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