Sharif Digital Repository

The Yau-Tian-Donaldson conjecture is a challenging problem in complex geometry which currently caught the attention of some birational geometers. This conjecture is about a formulation of the problem of finding the best metric over a Kahler manifold in terms of an asymptotic GIT stability condition. The first stability condition was proposed by Mumford in ICM 1962 which surprisingly just needs the vector bundle to be“more ample” among its subbundles. Another important theorem by Narasimhan and seshadri provides a connection between the slope stability and the existence constant curvature connections for the flat holomorphic vector bundles over compact Rieman surfaces. In 1983, Donaldson...