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2012 | 10 | 4 | 1455-1471
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Symplectic structures on moduli spaces of framed sheaves on surfaces

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EN
We provide generalizations of the notions of Atiyah class and Kodaira-Spencer map to the case of framed sheaves. Moreover, we construct closed two-forms on the moduli spaces of framed sheaves on surfaces. As an application, we define a symplectic structure on the moduli spaces of framed sheaves on some birationally ruled surfaces.
Twórcy
Bibliografia
  • [1] Atiyah M.F., Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc., 1957, 85, 181–207 http://dx.doi.org/10.1090/S0002-9947-1957-0086359-5
  • [2] Bănică C., Putinar M., Schumacher G., Variation der globalen Ext in Deformationen kompakter komplexer Räume, Math. Ann., 1980, 250(2), 135–155 http://dx.doi.org/10.1007/BF01364455
  • [3] Beauville A., Complex Algebraic Surfaces, London Math. Soc. Stud. Texts, 34, Cambridge University Press, Cambridge, 1996 http://dx.doi.org/10.1017/CBO9780511623936
  • [4] Bottacin F., Poisson structures on moduli spaces of sheaves over Poisson surfaces, Invent. Math., 1995, 121(2), 421–436 http://dx.doi.org/10.1007/BF01884307
  • [5] Bottacin F., Poisson structures on moduli spaces of framed vector bundles on surfaces, Math. Nachr., 2000, 220, 33–44 http://dx.doi.org/10.1002/1522-2616(200012)220:1<33::AID-MANA33>3.0.CO;2-A
  • [6] Bruzzo U., Markushevish D., Moduli of framed sheaves on projective surfaces, Doc. Math., 2011, 16, 399–410
  • [7] Gasparim E., Liu C.-C.M., The Nekrasov conjecture for toric surfaces, Comm. Math. Phys., 2010, 293(3), 661–700 http://dx.doi.org/10.1007/s00220-009-0948-4
  • [8] Hartshorne R., Algebraic Geometry, Grad. Texts in Math., 52, Springer, New York-Heidelberg, 1977
  • [9] Huybrechts D., Lehn M., Stable pairs on curves and surfaces, J. Algebraic Geom., 1995, 4(1), 67–104
  • [10] Huybrechts D., Lehn M., Framed modules and their moduli, Internat. J. Math., 1995, 6(2), 297–324 http://dx.doi.org/10.1142/S0129167X9500050X
  • [11] Huybrechts D., Lehn M., The Geometry of Moduli Spaces of Sheaves, 2nd ed., Cambridge Math. Lib., Cambridge University Press, Cambridge, 2010 http://dx.doi.org/10.1017/CBO9780511711985
  • [12] Illusie L., Complexe Cotangent et Déformations. I, Lecture Notes in Math., 239, Springer, Berlin-New York, 1971
  • [13] Illusie L., Complexe Cotangent et Déformations. II, Lecture Notes in Math., 283, Springer, Berlin-New York, 1972
  • [14] Lehn M., Modulräume gerahmter Vektorbündel, PhD thesis, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, 1992, Bonner Math. Schriften, 241, Universität Bonn, Mathematisches Institut, Bonn, 1993
  • [15] Maakestad H., On jets, extensions and characteristic classes. I, J. Gen. Lie Theory Appl., 2010, 4, #G091101
  • [16] Mukai S., Symplectic structure of the moduli space of sheaves on an abelian or K3 surface, Invent. Math., 1984, 77(1), 101–116 http://dx.doi.org/10.1007/BF01389137
  • [17] Mukai S., Moduli of vector bundles on K3 surfaces and symplectic manifolds, Sūgaku, 1987, 39(3), 216–235
  • [18] Nakajima H., Lectures on Hilbert schemes of points on surfaces, Univ. Lecture Ser., 18, American Mathematical Society, Providence, 1999
  • [19] Nevins T.A., Representability for some moduli stacks of framed sheaves, Manuscripta Math., 2002, 109(1), 85–91 http://dx.doi.org/10.1007/s00229-002-0290-z
  • [20] Nevins T.A., Moduli spaces of framed sheaves on certain ruled surfaces over elliptic curves, Internat. J. Math., 2002, 13(10), 1117–1151 http://dx.doi.org/10.1142/S0129167X02001599
  • [21] O’Grady K.G., Algebro-geometric analogues of Donaldson’s polynomials, Invent. Math., 1992, 107(2), 351–395 http://dx.doi.org/10.1007/BF01231894
  • [22] Ran Z., On the local geometry of moduli spaces of locally free sheaves, In: Moduli of Vector Bundles, Sanda-Kyoto, 1994, Lecture Notes in Pure and Appl. Math., 179, Marcel Dekker, New York, 1996
  • [23] Rava C., ADHM Data for Framed Sheaves on Hirzebruch Surfaces, PhD thesis, SISSA, Trieste, 2012
  • [24] Sala F., Some Topics in the Geometry of Framed Sheaves and their Moduli Spaces, PhD thesis, SISSA, Trieste and Université Lille 1, 2011
  • [25] Tyurin A.N., Symplectic structures on the moduli spaces of vector bundles on algebraic surfaces with p g > 0, Math. USSR-Izv., 1989, 33(1), 139–177 http://dx.doi.org/10.1070/IM1989v033n01ABEH000818
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Bibliografia
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bwmeta1.element.doi-10_2478_s11533-012-0063-1
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