CM Stability and the Generalized Futaki Invariant I
Algebraic Geometry
2008-04-23 v5
Abstract
Based on the Cayley, Grothendieck, Knudsen Mumford theory of determinants we extend the CM polarization to the Hilbert scheme. We identify the weight of this refined line bundle with the generalized Futaki invariant of Donaldson. We are able to conclude that CM stability implies K-Stability. An application of the Grothendieck Riemann Roch Theorem shows that this refined sheaf is isomorphic to the CM polarization introduced by Tian in 1994 on any closed, simply connected base .
Keywords
Cite
@article{arxiv.math/0605278,
title = {CM Stability and the Generalized Futaki Invariant I},
author = {Sean T. Paul and Gang Tian},
journal= {arXiv preprint arXiv:math/0605278},
year = {2008}
}
Comments
24 pages, fully rewritten, references added