KASS seminar

Abstract: We work on a Hermitian compact complex manifold (X,g) of dimension n whose associated 2-form is balanced, which is a slightly weaker condition than the 2-form being closed. In this context, a holomorphic Hermitian vector bundle (E,h) admits a Hermitian Yang-Mills connection if and only if it verifies an algebraic condition of stability. This important result is the Kobayashi-Hitchin correspondence. Stability depends on the class of the balanced metric g on X. During this talk, we try to understand the set of all balanced classes on X for which E is stable and more importantly, the behaviour of the associated Hermitian Yang-Mills connection. We show a continuity result when the class approaches a limit class for which E is destabilised.