中国科学院数学与系统科学研究院

数学研究所

学术报告

数论讨论班

Speaker: Jakob Glas (Leibniz Universität Hannover)

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

Time&Venue: 2024年12月6日（星期五）16:30-17:30 &Zoom Meeting ID: 859 6537 6871/Passcode: 788256

Abstract: 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.