2015/05/15 by Karmazyn, Joseph · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.1505.04049
In this paper we produce noncommutative algebras derived equivalent to deformations of schemes with tilting bundles. We do this in two settings, first proving that a tilting bundle on a scheme lifts to a tilting bundle on an infinitesimal deformations of that scheme and then expanding this result to ℂ^*-equivariant deformations over schemes with a good ℂ^*-action. In both these situations the endomorphism algebra of the lifted tilting bundle produces a deformation of the original endomorphism algebra, and this is a graded deformation in the ℂ^*-equivariant case. We apply our results to rational surface singularities, generalising the deformed preprojective algebras, and also to symplectic situations where the deformations produced are related to symplectic reflection algebras.