On an endomorphism conjecture of Fano manifolds of Picard number one

Abstract

A classical question in algebraic and complex dynamics asks for a description of a Fano manifold of Picard number one admitting a non-isomorphic surjective endomorphism. A well-known conjecture asserts that the projective space is the only possibility for the existence of such an endomorphism. In this talk, after a brief review of the known results and related questions, I would like to report our recent progress toward this conjecture in the following two cases: (1) the tangent bundle of the Fano manifold is big, or (2) its Fano index is large. The talk is based on joint works with Feng Shao.

About the speaker

仲国磊｜Institute for Basic Science

I am currently a Postdoctoral Research Fellow at Center for Complex Geometry of Institute for Basic Science in the Republic of Korea. I received my Ph.D. from National University of Singapore under the supervision of De-Qi Zhang in October 2021. Prior to that, I received my B.Sc. from East China Normal University in June 2017. I am working in algebraic geometry, birational geometry and their interaction with dynamical systems.