preprint draft Jakob Glas author d6423cba-dc74-11ea-a0a7-ee61689ff5fb Matthew Hase-Liu author TiBr department 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 eng 2412.1492310.48550/arXiv.2412.14923 https://research-explorer.ista.ac.at/record/18295 Glas J, Hase-Liu M. Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method. arXiv, <a href="https://doi.org/10.48550/arXiv.2412.14923">10.48550/arXiv.2412.14923</a>. J. Glas and M. Hase-Liu, “Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method,” <i>arXiv</i>. . 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> Glas, Jakob, and Matthew Hase-Liu. “Terminal Singularities of the Moduli Space of Curves on Low Degree Hypersurfaces and the Circle Method.” <i>ArXiv</i>, n.d. <a href="https://doi.org/10.48550/arXiv.2412.14923">https://doi.org/10.48550/arXiv.2412.14923</a>. J. Glas, M. Hase-Liu, ArXiv (n.d.). Glas, J., &#38; Hase-Liu, M. (n.d.). Terminal singularities of the moduli space of curves on low degree hypersurfaces and the circle method. <i>arXiv</i>. <a href="https://doi.org/10.48550/arXiv.2412.14923">https://doi.org/10.48550/arXiv.2412.14923</a> Glas, Jakob, and Matthew Hase-Liu. “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>. 190132025-02-07T12:04:11Z2026-07-29T10:05:58Z