turkmath.org

In this talk, we explore the connection between the enumerative geometry of rational curves on del Pezzo surfaces over a field k and the arithmetic properties of k. In particular, we classify the number of k-rational lines and conic families that can occur on del Pezzo surfaces of degrees 3 through 9 in terms of the Galois theory of k, and we give partial results in degrees 1 and 2. Our results generalize well-known theorems in the setting of smooth cubic surfaces. This is joint work in progress with Stephen McKean, Sam Streeter and Harkaran Uppal.