Tag: Qifeng Li

Let X be a smooth equivariant compactification of a symmetric space. In this talk, we will discuss when a minimal rational curve on X is the orbit closure of a 1-parameter group. In case the symmetric space is of group type, the answer is positive and moreover the VMRT is the closure of an adjoint orbit. This generalizes a result of Brion and Fu’s on wonderful compactifications to arbitrary equivariant compactifications. This is a joint work with Jun-Muk Hwang.

To each complex composition algebra A, there associates a projective symmetric manifold X(A) of Picard number 1. The vareity X(A) is closed related with Freudenthal’s Magic Square, which is a square starting from the adjiont varieties of F₄, E₆, E₇ and E₈. In a recent joint work with Yifei Chen and Baohua Fu, we obtain the deformation rigidity of X(A). In this talk, we will introduce the construction of X(A) from Freudenthal’s Magic Square, the geometric properties of them, and finally the deformation rigidity of X(A).

For a complex connected semisimple linear algebraic group G of adjoint type and of rank n, De Concini and Procesi constructed its wonderful compactification X, which is a smooth Fano variety of Picard number n enjoying many interesting properties. In this talk, we will show that the wonderful compactification X is rigid under Fano deformations. Namely, for any family of smooth Fano varieties over a connected base, if one fiber is isomorphic to X, then so are all other fibers. This answers a question raised by Bien and Brion in their work on the local rigidity of wonderful varieties.