Algebraic and Analytic K-Stability
Abstract
In this note we identify the leading terms of the (reduced) K-energy map with a universal linear combination of the principal and subdominant coefficients of the weight of the Hilbert point. This shows that the weight introduced by Donaldson in [SKD02] is just the weight of the CM-polarisation.The equivalence between the CM-(semi)stability and the K-(semi) stability follows from this. Also, using our previous work, we are able to describe this subdominant coefficient in terms of the weights of some generalised Chow forms, under a multiplicity free hypothesis on the degeneration. This is accomplished by introducing a parameter dependent lift of the CM-polarisation, and letting this parameter tend to infinity. This could be thought of as a ``quantized'' version of the virtual bundle introduced in [Tian94].
Cite
@article{arxiv.math/0405530,
title = {Algebraic and Analytic K-Stability},
author = {Sean T. Paul and Gang Tian},
journal= {arXiv preprint arXiv:math/0405530},
year = {2007}
}