CM Stability and the Generalized Futaki Invariant I
arXiv:math/0605278
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 .
24 pages, fully rewritten, references added
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Cited by in corpus (6)
- Lectures on Stability and Constant Scalar Curvature
- K-stability of constant scalar curvature Kähler manifolds
- Twisted cscK metrics and Kähler slope stability
- Deligne pairings and the Knudsen-Mumford expansion
- Multiplier ideal sheaves and geometric problems
- Test Configurations for K-Stability and Geodesic Rays