Essential dimension of parabolic bundles

Dinesh Valluri, The University of Western Ontario

Abstract

Essential dimension of a geometric object is roughly the number of algebraically independent parameters needed to define the object. In this thesis we give upper bounds for the essential dimension of parabolic bundles over a non-singular curve X of genus g greater than or equal to 2 using Borne's correspondence between parabolic bundles on a curve and vector bundles on a root stack. This is a generalization of the work of Biswas, Dhillon and Hoffmann on the essential dimension of vector bundles, by following their method for curves and adapting it to root stacks. In this process, we invoke the Riemann-Roch theorem of Toen for Deligne-Mumford stacks and use it to estimate the dimension of stack of parabolic bundles on X.