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arXiv · 1908.08260

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

Indranil Biswas·Tomas L. Gomez
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Abstract

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.

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Indranil Biswas, Tomas L. Gomez. 2019-08-22. Poisson structure on the moduli spaces of sheaves of pure dimension one on a surface. https://arxiv.org/abs/1908.08260

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