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arXiv · 1010.3597

The Calabi conjecture and K-stability

Yuji Odaka
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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.

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Yuji Odaka. 2010-10-18. The Calabi conjecture and K-stability. https://arxiv.org/abs/1010.3597

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