Biswas, Indranil ; Mukherjee, Avijit
(2003)
*On the symplectic structures on moduli space of stable sheaves over a K3 or abelian surface and on Hilbert scheme of points*
Archiv Der Mathematik, 80
(5).
pp. 507-515.
ISSN 0003-889X

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Official URL: http://www.springerlink.com/content/lc546wnq8aqm0r...

Related URL: http://dx.doi.org/10.1007/s00013-003-4613-4

## Abstract

Fix a smooth very ample curve C on a K3 or abelian surface X. Let M denote the moduli space of pairs of the form (F, s), where F is a stable sheaf over X whose Hilbert polynomial coincides with that of the direct image, by the inclusion map of C in X, of a line bundle of degree d over C, and s is a nonzero section of F. Assume d to be sufficiently large such that F has a nonzero section. The pullback of the Mukai symplectic form on moduli spaces of stable sheaves over X is a holomorphic 2-form on M. On the other hand, M has a map to a Hilbert scheme parametrizing 0-dimensional subschemes of X that sends (F, s) to the divisor, defined by s, on the curve defined by the support of F. We prove that the above 2-form on M coincides with the pullback of the symplectic form on the Hilbert scheme.

Item Type: | Article |
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Source: | Copyright of this article belongs to Birkhauser-Verlag. |

ID Code: | 3634 |

Deposited On: | 18 Oct 2010 10:17 |

Last Modified: | 18 Oct 2010 10:17 |

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