The Calabi conjecture and K-stability

Details The Calabi conjecture and K-stability The Calabi conjecture and K-stability

2010-10-18

arxiv.org/abs/1010.3597v3

Mathematics

Algebraic Geometry

16 pages, no figure. v2: minor revision, v3: title changed, re-editted (the latter half moved to arXiv:0807.1716 v4)

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

The Calabi conjecture and K-stability does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Calabi conjecture and K-stability, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Calabi conjecture and K-stability will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-306032