The projective space has maximal volume among all toric Kähler-Einstein manifolds

Abstract

We prove a conjecture saying that complex projective space has maximal volume (degree) among all toric Kaehler-Einstein manifolds of dimension n. The proof is inspired by our recent work on sharp Moser-Trudinger and Brezis-Merle type inequalities for the complex Monge-Ampere operator, but is essentially self-contained.

7 pages

References in corpus (3)

• An algorithm for the classification of smooth Fano polytopes
• Moser-Trudinger type inequalities for complex Monge-Ampère operators and Aubin's "hypothèse fondamentale"
• Examples of non-symmetric Kähler-Einstein toric Fano manifolds

Cited by in corpus (4)

• Optimal bounds for the volumes of Kähler-Einstein Fano manifolds
• Real Monge-Ampere equations and Kahler-Ricci solitons on toric log Fano varieties
• The volume of Kähler-Einstein Fano varieties and convex bodies
• A volume stability theorem on toric manifolds with positive Ricci curvature