Strong K-stability and asymptotic Chow-stability

Toshiki Mabuchi, Yasufumi Nitta

Published 2013-07-08, updated 2013-07-09Version 2

For a polarized algebraic manifold $(X,L)$, let $T$ be an algebraic torus in the group of all holomorphic automorphisms of $X$. Then strong relative K-stability will be shown to imply asymptotic relative Chow-stability. In particular, by taking $T$ to be trivial, we see that asymptotic Chow-stability follows from strong K-stability.