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http://dx.doi.org/10.4134/BKMS.b200928

ON BARYCENTRIC TRANSFORMATIONS OF FANO POLYTOPES  

Hwang, DongSeon (Department of Mathematics Ajou University)
Kim, Yeonsu (Department of Mathematics Ajou University)
Publication Information
Bulletin of the Korean Mathematical Society / v.58, no.5, 2021 , pp. 1247-1260 More about this Journal
Abstract
We introduce the notion of barycentric transformation of Fano polytopes, from which we can assign a certain type to each Fano polytope. The type can be viewed as a measure of the extent to which the given Fano polytope is close to be Kähler-Einstein. In particular, we expect that every Kähler-Einstein Fano polytope is of type B∞. We verify this expectation for some low dimensional cases. We emphasize that for a Fano polytope X of dimension 1, 3 or 5, X is Kähler-Einstein if and only if it is of type B∞.
Keywords
Barycentric transformation; Kahler-Einstein Fano polytope; symmetric Fano polytope;
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