Fano deformation rigidity of rational homogeneous spaces of submaximal Picard numbers
9:30 - 10:30
A Fano manifold is said to be rigid under Fano deformation if any deformation of it, which is also a Fano manifold, must be biholomorphic to itself. The deformation rigidity property of rational homogeneous spaces are get attentions since the series works of J.-M. Hwang and N. Mok on Picard number one cases (whose Kahler deformations are automatically Fano manifolds). Fano deformation rigidity of rational homogeneous spaces becomes more interesting since counterexamples of small Picard numbers are found. Recently A. Weber and J. A. Wisniewski proved that rational homogeneous spaces with maximal Picard numbers (i.e. complete flag manifolds) are rigid under Fano deformation. In this talk, I will present a program to verify the Fano deformation rigidity of a homogeneous space via that property of homogeneous submanifolds. Then the Fano deformation rigidity of rational homogeneous spaces of submaximal Picard numbers will be checked.
Equivariant Ulrich bundles and moduli spaces of Ulrich bundles
10:45 - 11:45
Ulrich bundles are vector bundles which enjoy many special features, and existence and properties of Ulrich bundles on a given algebraic variety tell us properties of the variety. Equivariant Ulrich bundles on rational homogeneous varieties of classical type were studied by many people. We prove that the only rational homogeneous varieties with Picard number 1 of the exceptional algebraic groups admitting irreducible equivariant Ulrich vector bundles are the (complex) Cayley plane E_6/P_1 and the E_7-adjoint variety E_7/P_1. And I will describe the moduli space of stable Ulrich bundles on the smooth Fano 3-fold of Picard number 1, degree 5 and index 2 using the moduli space of stable quiver representations. This talk is based on joint works with Kyoung-Seog Lee.