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Articles de revues sur le sujet « Hyper-Kähler manifolds »

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Auteur : Grafiati
Publié le 7 juillet 2024

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1

Dancer, A. « Hyper-Kähler manifolds ». Surveys in Differential Geometry 6, no 1 (2001) : 15–38. http://dx.doi.org/10.4310/sdg.2001.v6.n1.a2.

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2

Beckmann, Thorsten. « Derived categories of hyper-Kähler manifolds : extended Mukai vector and integral structure ». Compositio Mathematica 159, no 1 (janvier 2023) : 109–52. http://dx.doi.org/10.1112/s0010437x22007849.

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We introduce a linearised form of the square root of the Todd class inside the Verbitsky component of a hyper-Kähler manifold using the extended Mukai lattice. This enables us to define a Mukai vector for certain objects in the derived category taking values inside the extended Mukai lattice which is functorial for derived equivalences. As applications, we obtain a structure theorem for derived equivalences between hyper-Kähler manifolds as well as an integral lattice associated to the derived category of hyper-Kähler manifolds deformation equivalent to the Hilbert scheme of a K3 surface mimicking the surface case.
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3

Merker, Jochen. « On Almost Hyper-Para-Kähler Manifolds ». ISRN Geometry 2012 (8 mars 2012) : 1–13. http://dx.doi.org/10.5402/2012/535101.

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In this paper it is shown that a -dimensional almost symplectic manifold can be endowed with an almost paracomplex structure , , and an almost complex structure , , satisfying for , for and , if and only if the structure group of can be reduced from (or ) to . In the symplectic case such a manifold is called an almost hyper-para-Kähler manifold. Topological and metric properties of almost hyper-para-Kähler manifolds as well as integrability of are discussed. It is especially shown that the Pontrjagin classes of the eigenbundles of to the eigenvalues depend only on the symplectic structure and not on the choice of .
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4

Entov, Michael, et Misha Verbitsky. « Unobstructed symplectic packing for tori and hyper-Kähler manifolds ». Journal of Topology and Analysis 08, no 04 (8 septembre 2016) : 589–626. http://dx.doi.org/10.1142/s1793525316500229.

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Let [Formula: see text] be a closed symplectic manifold of volume [Formula: see text]. We say that the symplectic packings of [Formula: see text] by balls are unobstructed if any collection of disjoint symplectic balls (of possibly different radii) of total volume less than [Formula: see text] admits a symplectic embedding to [Formula: see text]. In 1994, McDuff and Polterovich proved that symplectic packings of Kähler manifolds by balls can be characterized in terms of the Kähler cones of their blow-ups. When [Formula: see text] is a Kähler manifold which is not a union of its proper subvarieties (such a manifold is called Campana simple), these Kähler cones can be described explicitly using the Demailly and Paun structure theorem. We prove that for any Campana simple Kähler manifold, as well as for any manifold which is a limit of Campana simple manifolds in a smooth deformation, the symplectic packings by balls are unobstructed. This is used to show that the symplectic packings by balls of all even-dimensional tori equipped with Kähler symplectic forms and of all hyper-Kähler manifolds of maximal holonomy are unobstructed. This generalizes a previous result by Latschev–McDuff–Schlenk. We also consider symplectic packings by other shapes and show, using Ratner’s orbit closure theorem, that any even-dimensional torus equipped with a Kähler form whose cohomology class is not proportional to a rational one admits a full symplectic packing by any number of equal polydisks (and, in particular, by any number of equal cubes).
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5

Alekseevsky, D. V., V. Cortés et T. Mohaupt. « Conification of Kähler and Hyper-Kähler Manifolds ». Communications in Mathematical Physics 324, no 2 (6 octobre 2013) : 637–55. http://dx.doi.org/10.1007/s00220-013-1812-0.

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6

GOTO, RYUSHI. « On toric hyper-Kähler manifolds given by the hyper-Kähler quotient method ». International Journal of Modern Physics A 07, supp01a (avril 1992) : 317–38. http://dx.doi.org/10.1142/s0217751x92003835.

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7

Krivonos, S. O., et A. V. Shcherbakov. « Hyper-Kähler manifolds and nonlinear supermultiplets ». Physics of Particles and Nuclei Letters 4, no 1 (février 2007) : 55–59. http://dx.doi.org/10.1134/s1547477107010104.

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8

Goto, R. « On hyper-Kähler manifolds of typeA ∞ ». Geometric and Functional Analysis 4, no 4 (juillet 1994) : 424–54. http://dx.doi.org/10.1007/bf01896403.

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9

CAPPELLETTI MONTANO, BENIAMINO, ANTONIO DE NICOLA et GIULIA DILEO. « THE GEOMETRY OF 3-QUASI-SASAKIAN MANIFOLDS ». International Journal of Mathematics 20, no 09 (septembre 2009) : 1081–105. http://dx.doi.org/10.1142/s0129167x09005662.

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3-quasi-Sasakian manifolds were studied systematically by the authors in a recent paper as a suitable setting unifying 3-Sasakian and 3-cosymplectic geometries. This paper throws new light on their geometric structure which appears to be generally richer compared to the 3-Sasakian subclass. In fact, it turns out that they are multiply foliated by four distinct fundamental foliations. The study of the transversal geometries with respect to these foliations allows us to link the 3-quasi-Sasakian manifolds to the more famous hyper-Kähler and quaternionic-Kähler geometries. Furthermore, we strongly improve the splitting results previously obtained; we prove that any 3-quasi-Sasakian manifold of rank 4l + 1 is 3-cosymplectic and any 3-quasi-Sasakian manifold of maximal rank is 3-α-Sasakian.
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10

BERGSHOEFF, ERIC, STEFAN VANDOREN et ANTOINE VAN PROEYEN. « THE IDENTIFICATION OF CONFORMAL HYPERCOMPLEX AND QUATERNIONIC MANIFOLDS ». International Journal of Geometric Methods in Modern Physics 03, no 05n06 (septembre 2006) : 913–32. http://dx.doi.org/10.1142/s0219887806001521.

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We review the map between hypercomplex manifolds that admit a closed homothetic Killing vector (i.e. "conformal hypercomplex" manifolds) and quaternionic manifolds of one dimension less. This map is related to a method for constructing supergravity theories using superconformal techniques. An explicit relation between the structure of these manifolds is presented, including curvatures and symmetries. An important role is played by "ξ transformations," relating connections on quaternionic manifolds, and a new type "[Formula: see text] transformations" relating complex structures on conformal hypercomplex manifolds. In this map, the subclass of conformal hyper-Kähler manifolds is mapped to quaternionic-Kähler manifolds.
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11

Yang, Qilin. « Vanishing Theorems on Compact Hyper-kähler Manifolds ». Geometry 2014 (16 février 2014) : 1–14. http://dx.doi.org/10.1155/2014/243236.

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We prove that if B is a k-positive holomorphic line bundle on a compact hyper-kähler manifold M, then HpM,Ωq⊗B=0 for P>n+[k/2] with q a nonnegative integer. In a special case, k=0 and q=0, we recover a vanishing theorem of Verbitsky’s with a little stronger assumption.
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12

Houghton, Conor J. « New hyper-Kähler manifolds by fixing monopoles ». Physical Review D 56, no 2 (15 juillet 1997) : 1220–27. http://dx.doi.org/10.1103/physrevd.56.1220.

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13

Gauntlett, J. P., G. W. Gibbons, G. Papadopoulos et P. K. Townsend. « Hyper-Kähler manifolds and multiply intersecting branes ». Nuclear Physics B 500, no 1-3 (septembre 1997) : 133–62. http://dx.doi.org/10.1016/s0550-3213(97)00335-0.

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14

Kollár, János, Radu Laza, Giulia Saccà et Claire Voisin. « Remarks on degenerations of hyper-Kähler manifolds ». Annales de l'Institut Fourier 68, no 7 (2018) : 2837–82. http://dx.doi.org/10.5802/aif.3228.

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15

Ivanov, Stefan, Ivan Minchev et Dimiter Vassilev. « Quaternionic contact hypersurfaces in hyper-Kähler manifolds ». Annali di Matematica Pura ed Applicata (1923 -) 196, no 1 (27 avril 2016) : 245–67. http://dx.doi.org/10.1007/s10231-016-0571-x.

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16

Ivanov, Stefan, Ivan Minchev et Dimiter Vassilev. « Non-Umbilical Quaternionic Contact Hypersurfaces in Hyper-Kähler Manifolds ». International Mathematics Research Notices 2019, no 18 (23 novembre 2017) : 5649–73. http://dx.doi.org/10.1093/imrn/rnx279.

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Abstract It is shown that any compact quaternionic contact (qc) hypersurfaces in a hyper-Kähler manifold which is not totally umbilical has an induced qc structure, locally qc homothetic to the standard 3-Sasakian sphere. In the non-compact case, it is proved that a seven-dimensional everywhere non-umbilical qc-hypersurface embedded in a hyper-Kähler manifold is qc-conformal to a qc-Einstein structure which is locally qc-equivalent to the 3-Sasakian sphere, the quaternionic Heisenberg group or the hyperboloid.
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17

Figueroa-O'Farrill, J. M., C. Köhl et B. Spence. « Supersymmetry and the cohomology of (hyper) Kähler manifolds ». Nuclear Physics B 503, no 3 (octobre 1997) : 614–26. http://dx.doi.org/10.1016/s0550-3213(97)00548-8.

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18

Rozansky, L., et E. Witten. « Hyper-Kähler geometry and invariants of three-manifolds ». Selecta Mathematica 3, no 3 (septembre 1997) : 401–58. http://dx.doi.org/10.1007/s000290050016.

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19

Howe, P. S., et G. Papadopoulos. « Twistor spaces for hyper-Kähler manifolds with torsion ». Physics Letters B 379, no 1-4 (juin 1996) : 80–86. http://dx.doi.org/10.1016/0370-2693(96)00393-0.

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20

Hitchin, Nigel, et Justin Sawon. « Curvature and characteristic numbers of hyper-Kähler manifolds ». Duke Mathematical Journal 106, no 3 (février 2001) : 599–615. http://dx.doi.org/10.1215/s0012-7094-01-10637-6.

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21

Goto, Ryushi. « On Hyper-Kähler Manifolds of Type A ∞ and D ∞ ». Communications in Mathematical Physics 198, no 2 (1 novembre 1998) : 469–91. http://dx.doi.org/10.1007/s002200050485.

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22

Salamon, S. M. « On the cohomology of Kahler and hyper-Kähler manifolds ». Topology 35, no 1 (janvier 1996) : 137–55. http://dx.doi.org/10.1016/0040-9383(95)00006-2.

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23

Entov, Michael, et Misha Verbitsky. « Unobstructed symplectic packing for tori and hyper-Kähler manifolds ». Journal of Topology and Analysis 11, no 01 (27 février 2019) : 249–50. http://dx.doi.org/10.1142/s1793525318920012.

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24

Kunikawa, Keita, et Ryosuke Takahashi. « Convergence of mean curvature flow in hyper-Kähler manifolds ». Pacific Journal of Mathematics 305, no 2 (29 avril 2020) : 667–91. http://dx.doi.org/10.2140/pjm.2020.305.667.

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25

Bergeron, Nicolas, et Zhiyuan Li. « Tautological classes on moduli spaces of hyper-Kähler manifolds ». Duke Mathematical Journal 168, no 7 (mai 2019) : 1179–230. http://dx.doi.org/10.1215/00127094-2018-0063.

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26

Benyounes, M., E. Loubeau et R. Pantilie. « Harmonic morphisms and moment maps on hyper-Kähler manifolds ». manuscripta mathematica 153, no 3-4 (27 octobre 2016) : 373–88. http://dx.doi.org/10.1007/s00229-016-0894-3.

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27

De Smedt, Vivian. « Decomposition of the curvature tensor of hyper-Kähler manifolds ». Letters in Mathematical Physics 30, no 2 (février 1994) : 105–17. http://dx.doi.org/10.1007/bf00939698.

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28

Biswas, Indranil, et Graeme Wilkin. « Anti-holomorphic involutive isometry of hyper-Kähler manifolds and branes ». Journal of Geometry and Physics 88 (février 2015) : 52–55. http://dx.doi.org/10.1016/j.geomphys.2014.11.001.

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29

Cao, Yalong, et Naichung Conan Leung. « Mukai flops and Plücker-type formulas for hyper-Kähler manifolds ». Proceedings of the American Mathematical Society 148, no 10 (20 juillet 2020) : 4119–35. http://dx.doi.org/10.1090/proc/15120.

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30

Hattori, Kota. « The Volume Growth of Hyper-Kähler Manifolds of Type A ∞ ». Journal of Geometric Analysis 21, no 4 (5 août 2010) : 920–49. http://dx.doi.org/10.1007/s12220-010-9173-9.

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31

OGUISO, KEIJI. « NO COHOMOLOGICALLY TRIVIAL NONTRIVIAL AUTOMORPHISM OF GENERALIZED KUMMER MANIFOLDS ». Nagoya Mathematical Journal 239 (5 novembre 2018) : 110–22. http://dx.doi.org/10.1017/nmj.2018.29.

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For a hyper-Kähler manifold deformation equivalent to a generalized Kummer manifold, we prove that the action of the automorphism group on the total Betti cohomology group is faithful. This is a sort of generalization of a work of Beauville and a more recent work of Boissière, Nieper-Wisskirchen, and Sarti, concerning the action of the automorphism group of a generalized Kummer manifold on the second cohomology group.
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32

Cortés, Vicente. « On hyper Kähler manifolds associated to Lagrangian Kähler submanifolds of $T^\ast \mathbb \{C\}^n$ ». Transactions of the American Mathematical Society 350, no 8 (1998) : 3193–205. http://dx.doi.org/10.1090/s0002-9947-98-02156-4.

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33

Bergeron, Nicolas, et Zhiyuan Li. « Complement to Tautological classes on moduli spaces of hyper-Kähler manifolds ». Annales de la Faculté des sciences de Toulouse : Mathématiques 32, no 5 (16 mai 2024) : 839–54. http://dx.doi.org/10.5802/afst.1755.

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34

LAAMARA, RACHID AHL, ADIL BELHAJ, LUIS J. BOYA et ANTONIO SEGUI. « ON LOCAL F-THEORY GEOMETRIES AND INTERSECTING D7-BRANES ». International Journal of Geometric Methods in Modern Physics 06, no 07 (novembre 2009) : 1207–20. http://dx.doi.org/10.1142/s0219887809004181.

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We discuss local F-theory geometries and their gauge theory dualities in terms of intersecting D7-branes wrapped four-cycles in Type IIB superstring. The manifolds are built as elliptic K3 surface fibrations over intersecting F0 = CP1 × CP1 base geometry according to ADE Dynkin Diagrams. The base is obtained by blowing up the extended ADE hyper-Kähler singularities of eight-dimensional manifolds considered as sigma model target spaces with eight supercharges. The resulting gauge theory of such local F-theory models are given in terms of Type IIB D7-branes wrapped intersecting F0. The four-dimensional N = 1 anomaly cancelation requirement translates into a condition on the associated affine Lie algebras.
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35

Thompson, George. « A Geometric Interpretation of the χ y Genus¶on Hyper-Kähler Manifolds ». Communications in Mathematical Physics 212, no 3 (août 2000) : 649–52. http://dx.doi.org/10.1007/s002200000230.

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36

Hattori, Kota. « New examples of compact special lagrangian submanifolds embedded in hyper-Kähler manifolds ». Journal of Symplectic Geometry 17, no 2 (2019) : 301–35. http://dx.doi.org/10.4310/jsg.2019.v17.n2.a1.

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37

Kurnosov, N. M. « An inequality for Betti numbers of hyper-Kähler manifolds of dimension 6 ». Mathematical Notes 99, no 1-2 (janvier 2016) : 330–34. http://dx.doi.org/10.1134/s0001434616010363.

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38

BELHAJ, ADIL, PABLO DIAZ, MARIA PILAR GARCIA DEL MORAL et ANTONIO SEGUI. « ON CHERN–SIMONS QUIVERS AND TORIC GEOMETRY ». International Journal of Geometric Methods in Modern Physics 09, no 07 (7 septembre 2012) : 1250050. http://dx.doi.org/10.1142/s0219887812500508.

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We discuss a class of three-dimensional [Formula: see text] Chern–Simons (CS) quiver gauge models obtained from M-theory compactifications on singular complex four-dimensional hyper-Kähler (HK) manifolds, which are realized explicitly as a cotangent bundle over two-Fano toric varieties V2. The corresponding CS gauge models are encoded in quivers similar to toric diagrams of V2. Using toric geometry, it is shown that the constraints on CS levels can be related to toric equations determining V2.
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39

Markman, Eyal. « Rational Hodge isometries of hyper-Kähler varieties of type are algebraic ». Compositio Mathematica 160, no 6 (7 mai 2024) : 1261–303. http://dx.doi.org/10.1112/s0010437x24007048.

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Let $X$ and $Y$ be compact hyper-Kähler manifolds deformation equivalent to the Hilbert scheme of length $n$ subschemes of a $K3$ surface. A class in $H^{p,p}(X\times Y,{\mathbb {Q}})$ is an analytic correspondence, if it belongs to the subring generated by Chern classes of coherent analytic sheaves. Let $f:H^2(X,{\mathbb {Q}})\rightarrow H^2(Y,{\mathbb {Q}})$ be a rational Hodge isometry with respect to the Beauville–Bogomolov–Fujiki pairings. We prove that $f$ is induced by an analytic correspondence. We furthermore lift $f$ to an analytic correspondence $\tilde {f}: H^*(X,{\mathbb {Q}})[2n]\rightarrow H^*(Y,{\mathbb {Q}})[2n]$ , which is a Hodge isometry with respect to the Mukai pairings and which preserves the gradings up to sign. When $X$ and $Y$ are projective, the correspondences $f$ and $\tilde {f}$ are algebraic.
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40

ANSELMI, DAMIANO, MARCO BILLÓ, PIETRO FRÉ, ALBERTO ZAFFARONI et LUCIANO GIRARDELLO. « ALE MANIFOLDS AND CONFORMAL FIELD THEORIES ». International Journal of Modern Physics A 09, no 17 (10 juillet 1994) : 3007–57. http://dx.doi.org/10.1142/s0217751x94001199.

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We address the problem of constructing the family of (4,4) theories associated with the σ model on a parametrized family ℳζ of asymptotically locally Euclidean (ALE) manifolds. We rely on the ADE classification of these manifolds and on their construction as hyper-Kähler quotients, due to Kronheimer. By so doing we are able to define the family of (4,4) theories corresponding to a ℳζ family of ALE manifolds as the deformation of a solvable orbifold C2/Γ conformal field theory, Γ being a Kleinian group. We discuss the relation between the algebraic structure underlying the topological and metric properties of self-dual four-manifolds and the algebraic properties of nonrational (4,4) theories admitting an infinite spectrum of primary fields. In particular, we identify the Hirzebruch signature τ with the dimension of the local polynomial ring [Formula: see text] associated with the ADE singularity, with the number of nontrivial conjugacy classes in the corresponding Kleinian group and with the number of short representations of the (4,4) theory minus four.
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41

BELHAJ, A., N. E. FAHSSI, E. H. SAIDI et A. SEGUI. « EMBEDDING FRACTIONAL QUANTUM HALL SOLITONS IN M-THEORY COMPACTIFICATIONS ». International Journal of Geometric Methods in Modern Physics 08, no 07 (novembre 2011) : 1507–18. http://dx.doi.org/10.1142/s0219887811005762.

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We engineer U(1)n Chern–Simons type theories describing fractional quantum Hall solitons (QHS) in 1 + 2 dimensions from M-theory compactified on eight-dimensional hyper-Kähler manifolds as target space of N = 4 sigma model. Based on M-theory/type IIA duality, the systems can be modeled by considering D6-branes wrapping intersecting Hirzebruch surfaces F0's arranged as ADE Dynkin Diagrams and interacting with higher-dimensional R-R gauge fields. In the case of finite Dynkin quivers, we recover well known values of the filling factor observed experimentally including Laughlin, Haldane and Jain series.
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42

BILLÓ, MARCO, PIETRO FRÈ, ALBERTO ZAFFARONI et LUCIANO GIRARDELLO. « GRAVITATIONAL INSTANTONS IN HETEROTIC STRING THEORY : THE H-MAP AND THE MODULI DEFORMATIONS OF (4,4) SUPERCONFORMAL THEORIES ». International Journal of Modern Physics A 08, no 14 (10 juin 1993) : 2351–418. http://dx.doi.org/10.1142/s0217751x9300093x.

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We study the problem of string propagation in a general instanton background for the case of the complete heterotic superstring. We define the concept of generalized hyper-Kähler manifolds and we relate it to (4,4) superconformal theories. We propose a generalized h-map construction that predicts a universal SU (6) symmetry for the modes of the string excitations moving in an instanton background. We also discuss the role of abstract N = 4 moduli and, applying it to the particular limit case of the solvable SU (2) × R instanton found by Callan et al., we show that it admits deformations and corresponds to a point in a 16-dimensional moduli space. The geometrical characterization of the other spaces in the same moduli space remains an open problem.
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43

GRANTCHAROV, GUEO, et MISHA VERBITSKY. « CALIBRATIONS IN HYPER-KÄHLER GEOMETRY ». Communications in Contemporary Mathematics 15, no 02 (7 mars 2013) : 1250060. http://dx.doi.org/10.1142/s0219199712500605.

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We describe a family of calibrations arising naturally on a hyper-Kähler manifold M. These calibrations calibrate the holomorphic Lagrangian, holomorphic isotropic and holomorphic coisotropic subvarieties. When M is an HKT (hyper-Kähler with torsion) manifold with holonomy SL (n, ℍ), we construct another family of calibrations Φi, which calibrates holomorphic Lagrangian and holomorphic coisotropic subvarieties. The calibrations Φi are (generally speaking) not parallel with respect to any torsion-free connection on M.
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44

JOHANSEN, A. « TWISTING OF N=1 SUSY GAUGE THEORIES AND HETEROTIC TOPOLOGICAL THEORIES ». International Journal of Modern Physics A 10, no 30 (10 décembre 1995) : 4325–57. http://dx.doi.org/10.1142/s0217751x9500200x.

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It is shown that D=4N=1 SUSY Yang-Mills theory with an appropriate supermultiplet of matter can be twisted on a compact Kähler manifold. The conditions for cancellation of anomalies of BRST charge are found. The twisted theory has an appropriate BRST charge. We find a nontrivial set of physical operators defined as classes of the cohomology of this BRST operator. We prove that the physical correlators are independent of the external Kähler metric up to a power of a ratio of two Ray-Singer torsions for the Dolbeault cohomology complex on a Kähler manifold. The correlators of local physical operators turn out to be independent of antiholomorphic coordinates defined with a complex structure on the Kähler manifold. However, a dependence of the correlators on holomorphic coordinates can still remain. For a hyper-Kähler metric the physical correlators turn out to be independent of all coordinates of insertions of local physical operators.
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45

Abe, Mitsuko. « The Partition Function in the Four-Dimensional Schwarz-Type Topological Half-Flat Two-Form Gravity ». Modern Physics Letters A 12, no 06 (28 février 1997) : 381–92. http://dx.doi.org/10.1142/s021773239700039x.

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We derive the partition functions of the Schwarz-type four-dimensional topological half-flat two-form gravity model on K3-surface or T4 up to on-shell one-loop corrections. In this model the bosonic moduli spaces describe an equivalent class of a trio of the Einstein–Kähler forms (the hyper-Kähler forms). The integrand of the partition function is represented by the product of some [Formula: see text]-torsions. [Formula: see text]-torsion is the extension of R-torsion for the de Rham complex to that for the [Formula: see text]-complex of a complex analytic manifold.
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46

Gutowski, J., et G. Papadopoulos. « The dynamics of D3-brane dyons and toric hyper-Kähler manifold ». Nuclear Physics B 551, no 3 (juillet 1999) : 650–66. http://dx.doi.org/10.1016/s0550-3213(99)00222-9.

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47

Lin, Hsueh-Yung. « Lagrangian Constant Cycle Subvarieties in Lagrangian Fibrations ». International Mathematics Research Notices 2020, no 1 (8 février 2018) : 14–24. http://dx.doi.org/10.1093/imrn/rnx334.

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Abstract We show that the image of a dominant meromorphic map from an irreducible compact Calabi–Yau manifold X whose general fiber is of dimension strictly between 0 and $\dim X$ is rationally connected. Using this result, we construct for any hyper-Kähler manifold X admitting a Lagrangian fibration a Lagrangian constant cycle subvariety ΣH in X which depends on a divisor class H whose restriction to some smooth Lagrangian fiber is ample. If $\dim X = 4$, we also show that up to a scalar multiple, the class of a zero-cycle supported on ΣH in CH0(X) depend neither on H nor on the Lagrangian fibration (provided b2(X) ≥ 8).
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48

Floccari, Salvatore. « Sixfolds of generalized Kummer type and K3 surfaces ». Compositio Mathematica 160, no 2 (5 janvier 2024) : 388–410. http://dx.doi.org/10.1112/s0010437x23007625.

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We prove that any hyper-Kähler sixfold $K$ of generalized Kummer type has a naturally associated manifold $Y_K$ of $\mathrm {K}3^{[3]}$ type. It is obtained as crepant resolution of the quotient of $K$ by a group of symplectic involutions acting trivially on its second cohomology. When $K$ is projective, the variety $Y_K$ is birational to a moduli space of stable sheaves on a uniquely determined projective $\mathrm {K}3$ surface $S_K$ . As an application of this construction we show that the Kuga–Satake correspondence is algebraic for the K3 surfaces $S_K$ , producing infinitely many new families of $\mathrm {K}3$ surfaces of general Picard rank $16$ satisfying the Kuga–Satake Hodge conjecture.
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49

Ootsuka, Takayoshi, Sayuri Miyagi, Yukinori Yasui et Shoji Zeze. « Anti-self-dual Maxwell solutions on hyper-Kähler manifold and N = 2 supersymmetric Ashtekar gravity ». Classical and Quantum Gravity 16, no 4 (1 janvier 1999) : 1305–12. http://dx.doi.org/10.1088/0264-9381/16/4/019.

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50

Tomberg, A. Yu. « Example of a Stable but Fiberwise Nonstable Bundle on the Twistor Space of a Hyper-Kähler Manifold ». Mathematical Notes 105, no 5-6 (mai 2019) : 941–45. http://dx.doi.org/10.1134/s000143461905033x.

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