The Limit of the Yang–Mills–Higgs Flow on Higgs Bundles

Abstract

In this article, we consider the gradient flow of the Yang–Mills–Higgs functional for Higgs pairs on a Hermitian vector bundle (E,H0) over a compact Kähler manifold (M,ω)⁠. We study the asymptotic behavior of the Yang–Mills–Higgs flow for Higgs pairs at infinity and show that the limiting Higgs sheaf is isomorphic to the double dual of the graded Higgs sheaves associated to the Harder–Narasimhan–Seshadri filtration of the initial Higgs bundle.

Locations

• International Mathematics Research Notices - View
• arXiv (Cornell University) - View - PDF