The ℂ*-actions on the moduli space of Higgs bundles

“Doc in Progress” is pleased to introduce you to:

• Miguel González - PhD Student Researcher - Instituto de Ciencias Matemáticas (ICMAT)

ℂ*-actions on complex algebraic varieties can be used to provide a better understanding of their topology and geometry. We will first showcase this in simple examples which are projective and hence limits at both directions (zero and infinity) always exist. Then we will introduce our main object of interest: moduli spaces of Higgs bundles. In this case the limit at infinity may not exist, motivating the definition of a "very stable" Higgs bundle. We will describe them in some cases after the recent work of Hausel and Hitchin, and Peón-Nieto. To conclude, we will announce work in progress joint with García-Prada and Hausel which classifies very stable G-Higgs bundles where the structure group G is an arbitrary complex semisimple Lie group.