날짜 : 2023-06-20 00:53
주제 :RicciprojectiveAlgebrahorosphericalKahlerEinsteinDuistermaat-Heckman
Abstract
A horospherical variety is a normal -variety such that a connected reductive algebraic group acts with an open orbit isomorphic to a torus bundle over a rational homogeneous manifold. The complex projective horospherical manifolds of Picard number one are classified by Pasquier, and it turned out that the automorphism groups of all nonhomogeneous ones are non-reductive, which implies that they admit no Kahler-Einstein metrics. As a numerical measure of the extent to which a Fano manifold is close to be Kahler-Einstein, we compute the greatest Ricci lower bounds of projective horospherical manifolds of Picard number one using the barycenter of each moment polytope with resprec to the Duistermaat-Heckam measure based on a recent work of Delcroix and Hultgren. This is joint work with DongSeon Hwang and Shin-Young Kim.