Matthew Hase-Liu: Terminality of moduli spaces of curves on low degree hypersurfaces via the circle method I

Speaker
Hase-Liu, Columbia

Abstract
We explain how to use ideas from analytic number theory to understand
the geometry of moduli spaces of curves on hypersurfaces. In particular,
we show that the moduli space of curves of fixed degree on a smooth
hypersurface of low degree only has terminal singularities. Using a
spreading out 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.