On the symplectic structures on moduli space of stable sheaves over a K3 or abelian surface and on Hilbert scheme of points |
| |
Authors: | Email author" target="_blank">Indranil?BiswasEmail author Email author" target="_blank">Avijit?MukherjeeEmail author |
| |
Institution: | (1) School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, 400005 Mumbay, India;(2) Naturwissenschaften, Max-Planck-Institute für Mathematik, Inselstr. 22-26, 04103 Leipzig, Germany |
| |
Abstract: | Fix a smooth very ample curve C on a K3 or abelian surface X. Let $ \mathcal{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 $ \mathcal{M} $. On the other hand, $ \mathcal{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 $ \mathcal{M} $ coincides with the pullback of the
symplectic form on the Hilbert scheme. |
| |
Keywords: | 53D30 14J60 14C05 |
本文献已被 SpringerLink 等数据库收录! |
|