Algebraic Geometry Seminar: Bounding the singular locus of the moduli of curves on a hypersurface, by Matthew Hase-Liu
February 9, 2026
3:00 PM - 3:50 PM
Matthew Hase-Liu (Columbia University): Bounding the singular locus of the moduli of curves on a hypersurface
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 RiedlYang 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. LehmannRiedlTanimoto's recent work on geometric Manins conjecture and 2. Sawin's work on Waring's problem from analytic number theory.
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Date posted
Feb 16, 2026
Date updated
Feb 16, 2026
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