Seminar in Real and Complex Geometry

Thursday, October 31, 2019, 16:00-18:00, Schreiber building, room 209

Karl Christ (Ben-Gurion University)

On irreducibility of Severi varieties of toric surfaces


Severi varieties parametrize irreducible curves of fixed geometric genus in a given linear system. They are classical objects that have been studied extensively. My talk will survey results concerning the irreducibility of such varieties for linear systems defined on toric surfaces. The case of the projective plane in characteristic zero was settled in the landmark paper of Harris in 1986. After recalling his approach, I will sketch further developments since then. Finally, I will report on ongoing work with Xiang He and Ilya Tyomkin, in which we use tropical geometry to study the question of irreducibility. In particular, we can prove irreducibility for the projective plane in positive characteristic. Time permitting, I will indicate some further directions we plan to investigate.