An arithmetic Abramovich--Bertram formula
Organizers
Speaker
Kirsten Wickelgren
Time
Thursday, May 30, 2024 10:00 PM - 11:00 PM
Venue
Online
Online
Zoom 638 227 8222
(BIMSA)
Abstract
Gromov--Witten invariants and Welschinger invariants count curves over the complex and real numbers. In joint work with J. Kass, M. Levine, and J. Solomon, we gave arithmetically meaningful counts of rational curves on smooth del Pezzo surfaces over general fields. This talk concerns how these invariants change under an algebraic analogue of surgery along a Lagrangian sphere. We allow certain del Pezzo surfaces to acquire a -2 curve and study deformations of curves to give an arithmetic enrichment of a formula due to D. Abramovich and A. Bertram over C and due to E. Brugallé and N. Puignau over R. This is joint work with Erwan Brugallé.