Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method Glas, Jakob Hase-Liu, Matthew 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. 2024 info:eu-repo/semantics/preprint doc-type:preprint text http://purl.org/coar/resource_type/c_816b https://research-explorer.ista.ac.at/record/19013 Glas J, Hase-Liu M. Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method. <i>arXiv</i>. doi:<a href="https://doi.org/10.48550/arXiv.2412.14923">10.48550/arXiv.2412.14923</a> eng info:eu-repo/semantics/altIdentifier/doi/10.48550/arXiv.2412.14923 info:eu-repo/semantics/altIdentifier/arxiv/2412.14923 info:eu-repo/semantics/openAccess