Rationally ruled surfaces admit noncommutative deformations parametrized by the Jacobian of an anticanonical curve, with derived categories and operator representations linking sheaves to difference equations.
Birational morphisms and Poisson moduli spaces
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
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.
fields
math.AG 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
The birational geometry of noncommutative surfaces
Rationally ruled surfaces admit noncommutative deformations parametrized by the Jacobian of an anticanonical curve, with derived categories and operator representations linking sheaves to difference equations.