Jaehyun Hong, Seoul National U., Seoul, Korea

Fano varieties of cones over rational homogeneous varieties

Abstract

Let G be a connected reductive algebraic group over C and let H be a closed subgroup. A homogeneous space G/H is said to be horospherical if H contains the unipotent radical of a Borel subgroup of G, or equivalently, G/H is isomorphic to a torus bundle over a rational homogeneous variety G/P. A normal G-variety is called horospherical if it contains an open dense G-orbit isomorphic to a horospherical homogeneous space G/H. For example, toric varieties and rational homogeneous varieties are horospherical. Cones over rational homogeneous varieties are horospherical, too.

In this talk we study Fano varieties of cones over rational homogeneous varieties. Then we use them to give embeddings of smooth horospherical varieties of Picard number one as linear sections of rational homogeneous varieties.