Poisson structure on the moduli spaces of sheaves of pure dimension one on a surface

Let S be a smooth complex projective surface equipped with a Poisson structure s and also a polarization H. The moduli space M_H(S,P) of stable sheaves on S having a fixed Hilbert polynomial P of degree one has a natural Poisson structure given by s, studied by Tyurin and Bottacin. We prove that the...

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Bibliographic Details
Main Authors Biswas, Indranil, Gomez, Tomas L
Format Journal Article
LanguageEnglish
Published 22.08.2019
Subjects
Mathematics - Algebraic Geometry
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Summary:Let S be a smooth complex projective surface equipped with a Poisson structure s and also a polarization H. The moduli space M_H(S,P) of stable sheaves on S having a fixed Hilbert polynomial P of degree one has a natural Poisson structure given by s, studied by Tyurin and Bottacin. We prove that the symplectic leaves of M_H(S,P) are the fibers of the natural map from it to the symmetric power of the effective divisor on S given by the singular locus of s.
DOI:10.48550/arxiv.1908.08260