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Статті в журналах з теми "Moduli spaces, framed sheaves, instantons"

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Автор: Grafiati

Опубліковано: 14 березня 2023

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1

HENNI, ABDELMOUBINE AMAR, MARCOS JARDIM, and RENATO VIDAL MARTINS. "ADHM CONSTRUCTION OF PERVERSE INSTANTON SHEAVES." Glasgow Mathematical Journal 57, no. 2 (December 18, 2014): 285–321. http://dx.doi.org/10.1017/s0017089514000305.

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Анотація:

AbstractWe present a construction of framed torsion free instanton sheaves on a projective variety containing a fixed line which further generalises the one on projective spaces. This is done by generalising the so called ADHM variety. We show that the moduli space of such objects is a quasi projective variety, which is fine in the case of projective spaces. We also give an ADHM categorical description of perverse instanton sheaves in the general case, along with a hypercohomological characterisation of these sheaves in the particular case of projective spaces.

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2

Scalise, Jacopo Vittorio. "Framed symplectic sheaves on surfaces." International Journal of Mathematics 29, no. 01 (January 2018): 1850007. http://dx.doi.org/10.1142/s0129167x18500076.

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A framed symplectic sheaf on a smooth projective surface [Formula: see text] is a torsion-free sheaf [Formula: see text] together with a trivialization on a divisor [Formula: see text] and a morphism [Formula: see text] satisfying some additional conditions. We construct a moduli space for framed symplectic sheaves on a surface, and present a detailed study for [Formula: see text]. In this case, the moduli space is irreducible and admits an ADHM-type description and a birational proper map onto the space of framed symplectic ideal instantons.

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3

HAUZER, MARCIN, та ADRIAN LANGER. "MODULI SPACES OF FRAMED PERVERSE INSTANTONS ON ℙ3". Glasgow Mathematical Journal 53, № 1 (25 серпня 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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4

Bartocci, Claudio, Valeriano Lanza, and Claudio L. S. Rava. "Moduli spaces of framed sheaves and quiver varieties." Journal of Geometry and Physics 118 (August 2017): 20–39. http://dx.doi.org/10.1016/j.geomphys.2016.10.011.

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5

Toda, Yukinobu. "Non-commutative thickening of moduli spaces of stable sheaves." Compositio Mathematica 153, no. 6 (April 26, 2017): 1153–95. http://dx.doi.org/10.1112/s0010437x17007047.

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We show that the moduli spaces of stable sheaves on projective schemes admit certain non-commutative structures, which we call quasi-NC structures, generalizing Kapranov’s NC structures. The completion of our quasi-NC structure at a closed point of the moduli space gives a pro-representable hull of the non-commutative deformation functor of the corresponding sheaf developed by Laudal, Eriksen, Segal and Efimov–Lunts–Orlov. We also show that the framed stable moduli spaces of sheaves have canonical NC structures.

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6

Ben-Zvi, David, and Thomas Nevins. "Perverse bundles and Calogero–Moser spaces." Compositio Mathematica 144, no. 6 (November 2008): 1403–28. http://dx.doi.org/10.1112/s0010437x0800359x.

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AbstractWe present a simple description of moduli spaces of torsion-free 𝒟-modules (𝒟-bundles) on general smooth complex curves, generalizing the identification of the space of ideals in the Weyl algebra with Calogero–Moser quiver varieties. Namely, we show that the moduli of 𝒟-bundles form twisted cotangent bundles to moduli of torsion sheaves on X, answering a question of Ginzburg. The corresponding (untwisted) cotangent bundles are identified with moduli of perverse vector bundles on T*X, which contain as open subsets the moduli of framed torsion-free sheaves (the Hilbert schemes T*X[n] in the rank-one case). The proof is based on the description of the derived category of 𝒟-modules on X by a noncommutative version of the Beilinson transform on P1.

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7

NEVINS, THOMAS A. "MODULI SPACES OF FRAMED SHEAVES ON CERTAIN RULED SURFACES OVER ELLIPTIC CURVES." International Journal of Mathematics 13, no. 10 (December 2002): 1117–51. http://dx.doi.org/10.1142/s0129167x02001599.

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Fix a ruled surface S obtained as the projective completion of a line bundle L on a complex elliptic curve C; we study the moduli problem of parametrizing certain pairs consisting of a sheaf ℰ on S and a map of ℰ to a fixed reference sheaf on S. We prove that the full moduli stack for this problem is representable by a scheme in some cases. Moreover, the moduli stack admits an action by the group C*, and we determine its fixed-point set, which leads to explicit formulas for the rational homology of the moduli space.

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8

Sala, Francesco. "Symplectic structures on moduli spaces of framed sheaves on surfaces." Central European Journal of Mathematics 10, no. 4 (May 2, 2012): 1455–71. http://dx.doi.org/10.2478/s11533-012-0063-1.

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9

von Flach, Rodrigo A., and Marcos Jardim. "Moduli spaces of framed flags of sheaves on the projective plane." Journal of Geometry and Physics 118 (August 2017): 138–68. http://dx.doi.org/10.1016/j.geomphys.2017.01.019.

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10

Szabo, Richard J. "Instantons, Topological Strings, and Enumerative Geometry." Advances in Mathematical Physics 2010 (2010): 1–70. http://dx.doi.org/10.1155/2010/107857.

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Анотація:

We review and elaborate on certain aspects of the connections between instanton counting in maximally supersymmetric gauge theories and the computation of enumerative invariants of smooth varieties. We study in detail three instances of gauge theories in six, four, and two dimensions which naturally arise in the context of topological string theory on certain noncompact threefolds. We describe how the instanton counting in these gauge theories is related to the computation of the entropy of supersymmetric black holes and how these results are related to wall-crossing properties of enumerative invariants such as Donaldson-Thomas and Gromov-Witten invariants. Some features of moduli spaces of torsion-free sheaves and the computation of their Euler characteristics are also elucidated.

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11

Markushevich, Dimitri, Alexander S. Tikhomirov, and Misha Verbitsky. "Editors’ preface for the topical issue “Instantons, coherent sheaves and their moduli spaces”." Central European Journal of Mathematics 10, no. 4 (May 31, 2012): 1185–87. http://dx.doi.org/10.2478/s11533-012-0075-x.

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12

Bartocci, Claudio, Valeriano Lanza, and Claudio L. S. Rava. "Corrigendum and addendum to “Moduli spaces of framed sheaves and quiver varieties”." Journal of Geometry and Physics 121 (November 2017): 176–79. http://dx.doi.org/10.1016/j.geomphys.2017.07.008.

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13

Bruzzo, Ugo, Rubik Poghossian, and Alessandro Tanzini. "Poincaré Polynomial of Moduli Spaces of Framed Sheaves on (Stacky) Hirzebruch Surfaces." Communications in Mathematical Physics 304, no. 2 (April 8, 2011): 395–409. http://dx.doi.org/10.1007/s00220-011-1231-z.

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14

Jardim, Marcos, and Misha Verbitsky. "Moduli spaces of framed instanton bundles on CP3 and twistor sections of moduli spaces of instantons on C2." Advances in Mathematics 227, no. 4 (July 2011): 1526–38. http://dx.doi.org/10.1016/j.aim.2011.03.012.

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15

Licata, Anthony, and Alistair Savage. "Vertex operators and the geometry of moduli spaces of framed torsion-free sheaves." Selecta Mathematica 16, no. 2 (December 11, 2009): 201–40. http://dx.doi.org/10.1007/s00029-009-0015-1.

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16

von Flach, Rodrigo A., Marcos Jardim, and Valeriano Lanza. "Obstruction theory for moduli spaces of framed flags of sheaves on the projective plane." Journal of Geometry and Physics 166 (August 2021): 104255. http://dx.doi.org/10.1016/j.geomphys.2021.104255.

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17

Cao, Yalong, Jacob Gross, and Dominic Joyce. "Orientability of moduli spaces of Spin(7)-instantons and coherent sheaves on Calabi–Yau 4-folds." Advances in Mathematics 368 (July 2020): 107134. http://dx.doi.org/10.1016/j.aim.2020.107134.

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18

Garbali, Alexandr, and Andrei Neguţ. "Computing the R-matrix of the quantum toroidal algebra." Journal of Mathematical Physics 64, no. 1 (January 1, 2023): 011702. http://dx.doi.org/10.1063/5.0120003.

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Анотація:

We consider the problem of the R-matrix of the quantum toroidal algebra [Formula: see text] in the Fock representation. Using the connection between the R-matrix R( u) ( u being the spectral parameter) and the theory of Macdonald operators, we obtain explicit formulas for R( u) in the operator and matrix forms. These formulas are expressed in terms of the eigenvalues of a certain Macdonald operator, which completely describe the functional dependence of R( u) on the spectral parameter u. We then consider the geometric R-matrix (obtained from the theory of K-theoretic stable bases on moduli spaces of framed sheaves), which is expected to coincide with R( u) and thus gives another approach to the study of the poles of the R-matrix as a function of u.

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19

Bartocci, Claudio, Claudio L. S. Rava, and Ugo Bruzzo. "Monads for framed sheaves on Hirzebruch surfaces." Advances in Geometry 15, no. 1 (January 1, 2015). http://dx.doi.org/10.1515/advgeom-2014-0027.

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AbstractWe define monads for framed torsion-free sheaves on Hirzebruch surfaces and use them to construct moduli spaces for these objects. These moduli spaces are smooth algebraic varieties, and we show that they are fine by constructing a universal monad.

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20

Cazzaniga, Alberto, and Andrea T. Ricolfi. "Framed sheaves on projective space and Quot schemes." Mathematische Zeitschrift, June 28, 2021. http://dx.doi.org/10.1007/s00209-021-02802-x.

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Анотація:

AbstractWe prove that, given integers $$m\ge 3$$ m ≥ 3 , $$r\ge 1$$ r ≥ 1 and $$n\ge 0$$ n ≥ 0 , the moduli space of torsion free sheaves on $${\mathbb {P}}^m$$ P m with Chern character $$(r,0,\ldots ,0,-n)$$ ( r , 0 , … , 0 , - n ) that are trivial along a hyperplane $$D \subset {\mathbb {P}}^m$$ D ⊂ P m is isomorphic to the Quot scheme $$\mathrm{Quot}_{{\mathbb {A}}^m}({\mathscr {O}}^{\oplus r},n)$$ Quot A m ( O ⊕ r , n ) of 0-dimensional length n quotients of the free sheaf $${\mathscr {O}}^{\oplus r}$$ O ⊕ r on $${\mathbb {A}}^m$$ A m . The proof goes by comparing the two tangent-obstruction theories on these moduli spaces.

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21

Koseki, Naoki. "Birational geometry of moduli spaces of perverse coherent sheaves on blow-ups." Mathematische Zeitschrift, May 20, 2021. http://dx.doi.org/10.1007/s00209-021-02774-y.

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Анотація:

AbstractIn order to study the wall-crossing formula of Donaldson type invariants on the blown-up plane, Nakajima–Yoshioka constructed a sequence of blow-up/blow-down diagrams connecting the moduli space of torsion free framed sheaves on projective plane, and that on its blow-up. In this paper, we prove that Nakajima–Yoshioka’s diagram realizes the minimal model program. Furthermore, we obtain a fully-faithful embedding between the derived categories of these moduli spaces.

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