Part 1 : Friday, 8 June, 2.00 p.m.
Part 2 : Monday, 11 June, 2.00 p.m.
A functorial approach to construction of moduli of sheaves
Harish Chandra Research Institute, Allahabad.
The problem of defining and constructing moduli of vector bundles on curve was studied by Mumford and Seshadri. A construction of moduli of pure sheaves on higher dimension cases was given by Simpson in characteristic 0 and Langer in positive characteristic. Simpson used GIT after embedding quot scheme in Grasmmannian with linearised group action. Using King's construction of moduli of representations, Alvarez-Consul and King gave another approach to construction of moduli of pure sheaves. They realized moduli of sheaves as closed subset of moduli of representations. In these talks we will present the construction of Alvarez-Consul and King for moduli of sheaves. If time permits we'll also discuss some applications of this approach to theta functions.