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arXiv · 2412.14923

Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method

Jakob Glas·Matthew Hase-Liu
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Abstract

We study the singularities of the moduli space of degree $e$ maps from smooth genus $g$ curves to an arbitrary smooth hypersurface of low degree. For $e$ large compared to $g$, we show that these moduli spaces have at worst terminal singularities. Our main approach is to study the jet schemes of these moduli spaces by developing a suitable form of the circle method.

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Jakob Glas, Matthew Hase-Liu. 2024-12-19. Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method. https://arxiv.org/abs/2412.14923

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