On Barycentric transformations of Fano polytopes
Bull. Korean Math. Soc.
Published online April 8, 2021
DongSeon Hwang and Yeonsu Kim
Ajou University
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 K\"ahler-Einstein. In particular, we expect that every K\"ahler-Einstein or symmetric Fano polytope is of type B_\infty. 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 K\"ahler-Einstein if and only if it is of type B_\infty.
Keywords : barycentric transformation, K\"ahler-Einstein Fano polytope, symmetric Fano polytope.
MSC numbers : 52B20, 52B15, 14M25, 32Q20
Full-Text :

   

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd