Moduli spaces of sheaves on surfaces: Hecke correspondences and representation theory

Abstract

© Springer Nature Switzerland AG 2019. In modern terms, enumerative geometry is the study of moduli spaces: instead of counting various geometric objects, one describes the set of such objects, which if lucky enough to enjoy good geometric properties is called a moduli space. For example, the moduli space of linear subspaces of 𝔸n is the Grassmannian variety, which is a classical object in representation theory. Its cohomology and intersection theory (as well as those of its more complicated cousins, the flag varieties) have long been studied in connection with the Lie algebras 𝔰 𝔩 n.