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arXiv · 2412.04618

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

Matthew Hase-Liu·Amal Mattoo
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Abstract

We show that the moduli space of degree $e$ maps from smooth genus $g \ge 1$ 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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Matthew Hase-Liu, Amal Mattoo. 2024-12-05. Non-smoothness of Moduli Spaces of Higher Genus Curves on Low Degree Hypersurfaces. https://arxiv.org/abs/2412.04618

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