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Birational morphisms and Poisson moduli spaces

Rains, Eric M. (2013) Birational morphisms and Poisson moduli spaces. , Pasadena, CA. (Submitted)

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We study birational morphisms between smooth projective surfaces that respect a given Poisson structure, with particular attention to induced birational maps between the (Poisson) moduli spaces of sheaves on those surfaces. In particular, to any birational morphism, we associate a corresponding "minimal lift" operation on sheaves of homological dimension ≤ 1, and study its properties. In particular, we show that minimal lift induces a stratification of the moduli space of simple sheaves on the codomain by open subspaces of the moduli space of simple sheaves on the domain, compatibly with the induced Poisson structures.

Item Type:Report or Paper (Discussion Paper)
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Record Number:CaltechAUTHORS:20170922-144027436
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81770
Deposited By: Tony Diaz
Deposited On:22 Sep 2017 22:11
Last Modified:03 Oct 2019 18:46

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