The Hitchin-Kobayashi correspondence states that the moduli space of stable vector bundles over a projective manifold coincides with the moduli space of Einstein-Hermitian vector bundles. Over the years, this result and its consequences have served as a motivation to relate the existence of metrics of constant curvature on polarized manifolds to an algebraic condition (K-stability).The correspondence between stable and Einstein-Hermitian vector bundles has a well-known generalization in the context of Higgs bundles, where one studies Hitchin's *harmonic bundle equations*. In this talk we will describe how to give an analogous construction in the category of polarized varieties, thus defining what a "Higgs field" should be in this context and studying a system of equations that naturally arises from the construction.

## An analogue of Hitchin's equations in the category of polarized varieties

Research Group:

Carlo Scarpa

Institution:

SISSA

Schedule:

Tuesday, January 21, 2020 - 16:00

Location:

A-134

Abstract: