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On the equality case in Ehrhart's volume conjecture | | Benjamin Nill
; Andreas Paffenholz
; | | Date: |
7 May 2012 | | Abstract: | Ehrhart’s conjecture proposes a sharp upper bound on the volume of a convex
body whose barycenter is its only interior lattice point. Recently, Berman and
Berndtsson proved this conjecture for a class of rational polytopes including
reflexive polytopes. In particular, they showed that the complex projective
space has the maximal anticanonical degree among all toric Kaehler-Einstein
Fano manifolds. In this note, we prove that projective space is the only such
toric manifold with maximal degree by proving its corresponding
convex-geometric statement. We also discuss a generalized version of Ehrhart’s
conjecture involving an invariant corresponding to the so-called greatest lower
bound on the Ricci curvature. | | Source: | arXiv, 1205.1270 | | Services: | Forum | Review | PDF | Favorites | |
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