Differential operators on Hitchin variety

2020/07/11 by Singh, Anoop
#14D06 #14F10 #32C38 #53C05 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2007.05699

Abstract

We introduce the notion of Hitchin variety over \C. Let L be a holomorphic line bundle over a Hitchin variety X. We investigate the space of all global sections of sheaf of differential operators \catD^k (L) and symmetric powers of sheaf of first order differential operators \catS^k(\catD¹ (L)) over X and show that for a projective Hithcin variety both the spaces are one dimensional. As an application, we show that the space \catC(L) of holomorphic connections on L does not admit any non-constant regular function.

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