Rigidity of complex projective manifolds
by ,
Thursday 26 September May 2024, 4:00 PM - 6:00 PM
Korea
A complex projective manifold X is said to be (globally) rigid under projective deformations if for any smooth projective morphism over a disc with one fiber biholomorphic to X, then all fibers are biholomorphic to X. For example, the projective space of dimension n is rigid by a classical result of Hirzebruch and Kodaira; the same holds for quadrics of dimension n at least 3 (Brieskorn and Hwang), but not for Hirzebruch surfaces. More generally, projective homogeneous varieties of Picard rank 1 were shown to be rigid by Hwang and Mok, with one (remarkable) exception.
The first part of the talk will discuss this notion of rigidity, its relation to infinitesimal (local) rigidity, and present some classical examples. The second part will survey the results of Hwang and Mok, and further recent developments about Fano almost homogeneous varieties with Picard rank one and projective homogeneous varieties of higher Picard rank. Finally, we will survey the varieties of minimal rational tangents as a main tool to prove the global rigidity.
Chairman of the first lecture: JaeHyouk Lee
Chairman of the second lecture: Samuel Boissière