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

2024/12/19 by Jakob Glas, Glas, Jakob, Matthew Hase-Liu +1 · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Algebraic and Geometric Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2412.14923

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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• Rational surfaces on low degree hypersurfaces
• A geometric determinant method and geometric dimension growth

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