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. |