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The volume of Kahler-Einstein varieties and convex bodies

Bo Berndtsson (Institutionen för matematiska vetenskaper, matematik) ; Robert Berman (Institutionen för matematiska vetenskaper, matematik)
Journal für die Reine und Angewandte Mathematik (0075-4102). Vol. 2017 (2017), 723, p. 127-152.
[Artikel, refereegranskad vetenskaplig]

We show that the complex projective space ℙnhas maximal degree (volume) among all n-dimensional Kähler-Einstein Fano manifolds admitting a non-trivial 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 ℂnof independent interest. The paper supersedes our previous preprint [5] concerning the case of toric Fano manifolds.

Denna post skapades 2016-02-02. Senast ändrad 2017-03-22.
CPL Pubid: 231588


Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)



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