Rencontres de théorie analytique des nombres

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

par Jakob Glas (Leibniz Universität Hannover)

Europe/Paris
Salle Grisvard, IHP, Paris

Salle Grisvard, IHP, Paris

Description

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. 

Organisé par

Régis de la Bretèche
Cathy Swaenepoel