5 papers · 1 filter
Betti bounds for spaces of curves on varieties and Manin's conjecture for quartic del Pezzo surfaces
Enhao Feng, Matthew Hase-Liu
We prove uniform exponential bounds for the compactly supported Betti numbers of spaces of morphisms from curves of fixed genus to projective varieties. For targets in a fixed proj…
A converse to geometric Manin's conjecture for general low degree hypersurfaces and Poincaré duality
Matthew Hase-Liu
Geometric Manin's conjecture predicts that components of the moduli space of curves on a Fano variety parametrizing non-free curves are pathological and arise from "accumulating" m…
Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method
Jakob Glas, Matthew Hase-Liu
We study the singularities of the moduli space of degree maps from smooth genus curves to an arbitrary smooth hypersurface of low degree. For large compared to , we…
Non-smoothness of Moduli Spaces of Higher Genus Curves on Low Degree Hypersurfaces
Matthew Hase-Liu, Amal Mattoo
We show that the moduli space of degree maps from smooth genus curves to an arbitrary low degree smooth hypersurface is singular when is large compared to . We…
A higher genus circle method and an application to geometric Manin's conjecture
Matthew Hase-Liu
Browning and Vishe used the Hardy-Littlewood circle method to show the moduli space of rational curves on smooth hypersurfaces of low degree is irreducible and of the expected dime…