Back to Algebraic Geometry Seminar: Fall 2025
Algebraic Geometry Seminar
Date: Tuesday, Sep 30, 2025
Time: 3:30PM - 4:30PM
Location: LCB 323
Phil Tosteson
UNC
Title |
Moduli of curves on del Pezzo surfaces and Manin's conjecture |
Abstract |
For a projective variety X defined over a finite field, the homology of the space of rational curves on X is closely related to the F_q(T) rational points on X. In particular, Manin’s conjecture for the asymptotic count of rational points on a Fano variety suggests a corresponding homological stability conjecture for moduli spaces of rational curves. We will discuss joint work with R. Das, B. Lehmann, and S. Tanimoto establishing both these conjectures in the case where X is a quartic del Pezzo surface. |
Algebraic Geometry