preprint submitted Jakob Glas author d6423cba-dc74-11ea-a0a7-ee61689ff5fb TiBr department Rational curves via function field analytic number theory project By developing a suitable version of the circle method, we show that the space of degree e rational curves on a smooth hypersurface of degree d has only canonical singularities provided its dimension is sufficiently large with respect to e and d. https://creativecommons.org/licenses/by/4.0/ 2024 eng 2405.1664810.48550/arXiv.2405.16648 https://research-explorer.ista.ac.at/record/19013 https://research-explorer.ista.ac.at/record/18132 J. Glas, ArXiv (n.d.). Glas J. Canonical singularities on moduli spaces of rational curves via the  circle method. arXiv, <a href="https://doi.org/10.48550/arXiv.2405.16648">10.48550/arXiv.2405.16648</a>. Glas, Jakob. “Canonical Singularities on Moduli Spaces of Rational Curves via the  Circle Method.” <i>ArXiv</i>, n.d. <a href="https://doi.org/10.48550/arXiv.2405.16648">https://doi.org/10.48550/arXiv.2405.16648</a>. Glas, J. (n.d.). Canonical singularities on moduli spaces of rational curves via the  circle method. <i>arXiv</i>. <a href="https://doi.org/10.48550/arXiv.2405.16648">https://doi.org/10.48550/arXiv.2405.16648</a> J. Glas, “Canonical singularities on moduli spaces of rational curves via the  circle method,” <i>arXiv</i>. . Glas J. Canonical singularities on moduli spaces of rational curves via the  circle method. <i>arXiv</i>. doi:<a href="https://doi.org/10.48550/arXiv.2405.16648">10.48550/arXiv.2405.16648</a> Glas, Jakob. “Canonical Singularities on Moduli Spaces of Rational Curves via the  Circle Method.” <i>ArXiv</i>, doi:<a href="https://doi.org/10.48550/arXiv.2405.16648">10.48550/arXiv.2405.16648</a>. 182952024-10-10T13:15:43Z2026-04-07T12:53:53Z