Hecke cycles associated to rank 2 twisted Higgs bundles on a curve

Abstract

Let X be a smooth complex projective curve of genus g and let L be a line bundle on X with deg L > 0. Let M be the moduli space of semistable rank 2 L-twisted Higgs bundles with trivial determinant on X. Let M-X be the moduli space of stable rank 2 L-twisted Higgs bundles with determinant O(-x) for some x is an element of X on X. We construct a cycle in the product of a stack of rational maps from nonsingular curves to M-X and Pic(2deg) (L)(X) by using Hecke modifications of a stable L-twisted Higgs bundle in M.