Seminar in Algebraic Geometry and Number Theory

Abstract: Following Segal's work on rational functions and its many extensions, we show that the space of holomorphic maps from Riemann surfaces to certain blowups of projective space has homological stability as the degree gets large. We also explore arithmetic applications to the Batyrev-Manin conjecture for del Pezzo surfaces, by applying the Grothendieck-Lefschetz trace formula to these topological results. The talk will be based on ongoing joint work with Brian Lehmann, Sho Tanimoto and Philip Tosteson.