Advances in Geometry
Managing Editor: Grundhöfer, Theo / Joswig, Michael
Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard
IMPACT FACTOR 2018: 0.789
CiteScore 2018: 0.73
SCImago Journal Rank (SJR) 2018: 0.329
Source Normalized Impact per Paper (SNIP) 2018: 0.908
Mathematical Citation Quotient (MCQ) 2017: 0.62
On the equality case in Ehrhart’s volume conjecture
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 Kähler- Einstein Fano manifolds.
In this note, we prove that projective space is the only such toric manifold with maximal degree by proving the 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.
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