Terminality of moduli spaces of curves on hypersurfaces via the circle method

by Jakob Glas (Leibniz Universität Hannover)

Monday Dec 9, 2024, 11:00 AM → 12:00 PM Europe/Paris

Salle Grisvard, IHP, Paris

I will report on joint work with Matthew Hase-Liu that shows that the moduli space of genus $g$ curves of degree $e$ on a smooth hypersurface of low degree only has terminal singularities, provided $e$ is sufficiently large with respect to $g$. Using a spreading argument together with a result of Mustata, we reduce the problem to counting points over finite fields on the jet schemes of these moduli spaces. We solve this counting problem by developing a suitable version of the circle method.