The volume of Kähler-Einstein Fano varieties and convex bodies

Details The volume of Kähler-Einstein Fano varieties and convex bodies The volume of Kähler-Einstein Fano varieties and convex bodies

2012-04-05

arxiv.org/abs/1204.1308v1

Mathematics

Differential Geometry

28 pages

Scientific paper

We show that the complex projective space has maximal degree (volume) among all n-dimensional Kahler-Einstein Fano manifolds admitting a holomorphic C^*-action with a finite number of fixed points. The toric version of this result, translated to the realm of convex geometry, thus confirms Ehrhart's volume conjecture for a large class of rational polytopes, including duals of lattice polytopes. The case of spherical varieties/multiplicity free symplectic manifolds is also discussed. The proof uses Moser-Trudinger type inequalities for Stein domains and also leads to criticality results for mean field type equations in C^n of independent interest. The paper supersedes our previous preprint concerning the case of toric Fano manifolds.

Affiliated with

Also associated with

No associations

Rating

The volume of Kähler-Einstein Fano varieties and convex bodies 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 volume of Kähler-Einstein Fano varieties and convex bodies, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The volume of Kähler-Einstein Fano varieties and convex bodies will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-213404