Birational morphisms and Poisson moduli spaces

2013/07/15 by Eric M. Rains, Rains, Eric M.
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1307.4032

openalex publication_date 2013/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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