Closed differential forms on moduli spaces of sheaves
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 u...
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| Formato: | article |
| Lenguaje: | EN FR IT |
| Publicado: |
Sapienza Università Editrice
2008
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/75bffad621b542abb08f3f1eb4677b67 |
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| Sumario: | 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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