Rendiconti di Matematica e delle Sue Applicazioni (Jan 2008)

Closed differential forms on moduli spaces of sheaves

  • Francesco Bottacin

Journal volume & issue
Vol. 28, no. 2
pp. 139 – 162

Abstract

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Let X be a smooth projective variety, and let M be a moduli space of stable sheaves on X. For any flat family E of coherent sheaves on X parametrized by a smooth scheme Y , and for any integer m, with 1 ≤ m ≤ dim X, we construct a closed differential form Ω=Ω_E on Y with values in H^m(X, O_X). By using the vector-valued differential form Ω we then prove that the choice of a (non-zero) differential m-form σ on X, σ ∈ H^0(X, Ω_m^X ), determines, in a natural way, a closed differential m-form Ω_σ on M.

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