December 12, 2018

                       N913, AMSS

9:30—10:30    Qifeng Li (KIAS)

Fano deformation rigidity of rational homogeneous spaces of submaximal Picard numbers

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.