Minseong Kwon, Automorphism groups of toroidal horospherical varieties

In the 1970s, Demazure studied the automorphism groups of two types of almost homogeneous varieties: rational homogeneous spaces and toric varieties. Especially, for a smooth complete toric variety, Demazure obtained a structure theorem for the connected automorphism group in terms of the so-called Demazure roots. In this talk, I will discuss the connected automorphism group of a smooth complete toroidal horospherical variety, which can be viewed as a fiber bundle over a rational homogeneous space with toric fibers. Namely, I will introduce a notion of roots as a generalization of the Demazure roots, and then utilize it to describe the structure of the connected automorphism group. As a consequence, a reductivity criterion for the connected automorphism group will be presented. This talk is based on a joint work with Lorenzo Barban and DongSeon Hwang.