On the Symplectic Structures on Moduli Space of Stable Sheaves over a K3 or Abelian Surface and on Hilbert Scheme of Points
نویسندگان
چکیده
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 Hilbert scheme.
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