Algebraic Geometry Seminar
Matthew Hase-Liu
Columbia University
Bounding the singular locus of the moduli of curves on a hypersurface
Abstract: The space of rational curves on a Fano variety X serves as a powerful tool for probing the geometry of X. Even for hypersurfaces, characterizing these spaces is difficult; however, work by Riedl–Yang established they are irreducible and have the expected dimension. In this talk, I will discuss another aspect, namely the singular locus. Specifically, I will show the singular locus of the moduli space of smooth degree e curves on a general low-degree hypersurface is small, i.e. has codimension growing linearly with e. This turns out to use a weird combination of 1. Lehmann–Riedl–Tanimoto's recent work on geometric Manin’s conjecture and 2. Sawin's work on Waring's problem from analytic number theory.
Monday February 9, 2026 at 3:00 PM in 636 SEO