Stability of Algebraic Manifolds
نویسندگان
چکیده
In this paper, we study the stability of non-singular projective varieties. We will prove a geometric criterion for a non-singular projective variety to be GIT stable in the Hilbert scheme, and then relate the Gieseker-Mumford stability of polarized manifolds to the behavior of heat kernels. We will also discuss the stability notion used by Viehweg, and state some new semi-positivity results of Hodge bundles. In the end, we find some of the methods we used to understand the semi-positivity can be applied to study various vanishing theorems. Thesis Supervisor: I. M. Singer Title: Professor of Mathematics, Institute Professor
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