Non-smoothness of Moduli Spaces of Higher Genus Curves on Low Degree Hypersurfaces

2024/12/05 by Hase-Liu, Matthew, Mattoo, Amal
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.04618

Abstract

We show that the moduli space of degree e maps from smooth genus g ≥ 1 curves to an arbitrary low degree smooth hypersurface is singular when e is large compared to g. We also give a lower bound for the dimension of the singular locus.

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