The Calabi conjecture and K-stability
arXiv:1010.3597
Abstract
We algebraically prove K-stability of polarized Calabi-Yau varieties and canonically polarized varieties with mild singularities. In particular, the} "stable varieties" introduced by Kollar-Shepherd-Barron and Alexeev, which form compact moduli space, are proven to be K-stable although it is well known that they are \textit{not} necessarily asymptotically (semi)stable. As a consequence, we have orbifold counterexamples, to the folklore conjecture "K-stability implies asymptotic stability". They have Kahler-Einstein (orbifold) metrics so the result of Donaldson does not hold for orbifolds.
16 pages, no figure. v2: minor revision, v3: title changed, re-editted (the latter half moved to arXiv:0807.1716 v4)
References in corpus (8)
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