The dimension of the moduli space of pointed algebraic curves of low genus

References

• Buchweitz, R.-O. (1980). On deformations of monomial curves. In: Demazure, M., Pinkham, H. C., Teissier, B., eds. Sminaire sur les Singularits des Surfaces. Lecture Notes in Mathematics, Vol. 777. Berlin, Heidelberg: Springer, pp. 205–220. DOI: 10.1007/BFb0085884.
   Google Scholar
• Bullock, E. M. (2014). Irreducibility and stable rationality of the loci of curves of genus at most six with a marked Weierstrass point. Proc. Am. Math. Soc. 142:1121–1132. DOI: 10.1090/S0002-9939-2014-11899-5.
   Web of Science ®Google Scholar
• Contiero, A., Stohr, K.-O. (2013). Upper bounds for the dimension of moduli spaces of curves with symmetric Weierstrass semigroups. J. London Math. Soc. 88:580–598. DOI: 10.1112/jlms/jdt034.
   Web of Science ®Google Scholar
• Contiero, A., Fontes, A. L., Stevens, J., Vargas, J. Q. (2021). On nonnegatively graded Weierstrass points. arXiv:2111.07721.
   Google Scholar
• Grayson, D. R., Stillman, M. E. Macaulay2, a software system for research in algebraic geometry. http://www.math.uiuc.edu/Macaulay2/
   Google Scholar
• Decker, W., Greuel, G.-M., Pfister, G., Schönemann, H. (2020). Singular 4-1-3 — A computer algebra system for polynomial computations. https://www.singular.uni-kl.de.
   Google Scholar
• Delgado, M., Garcia-Sanchez, P. A., Morais, J. (2022). NumericalSgps, A package for numerical semigroups, Version 1.3.1 (Refereed GAP package), https://gap-packages.github.io/numericalsgps.
   Google Scholar
• Greuel, G.-M. (1982). On deformation of curves and a formula of Deligne. In: Aroca, J. M., Buchweitz, R., Giusti, M., Merle, M., eds. Algebraic Geometry. Lecture Notes in Mathematics, Vol 961. Berlin, Heidelberg: Springer, pp. 141–168. DOI: 10.1007/BFb0071281.
   Google Scholar
• Haure, M. (1896). Recherches sur les points de Weierstrass d’une courbe plane algébrique. Ann. Sci. Éc. Norm. Supér. (3) 13:115–196. DOI: 10.24033/asens.426.
   Google Scholar
• Hauser, H. (1983). An algorithm of construction of the semiuniversal deformation of an isolated singularity. In: Singularities, Part 1 (Arcata, Calif., 1981), Proceedings of Symposia in Pure Mathematics, Vol. 40. Providence, RI: American Mathematical Society, pp. 567–573.
   Google Scholar
• Hauser, H. (1985). La construction de la déformation semi-universelle d’un germe de variété analytique complexe. Ann. Sci. École Norm. Sup. 18:1–56. DOI: 10.24033/asens.1483.
   Google Scholar
• Ilten, N. VersalDeformations: versal deformations and local Hilbert schemes. Version 3.0, A Macaulay2 package available at https://github.com/Macaulay2/M2/tree/master/M2/Macaulay2/packages
   Google Scholar
• Jong, T. de, Straten, D. van. (1990). A deformation theory for non-isolated singularities. Abh. Math. Sem. Univ. Hamburg 60:177–208. DOI: 10.1007/BF02941057.
   Web of Science ®Google Scholar
• Jong, T. de, Straten, D. van. (1990). Deformations of the normalization of hypersurfaces. Math. Ann. 288:527–547. DOI: 10.1007/BF01444547.
   Web of Science ®Google Scholar
• Jong, T. de, Straten, D. van. (1991). On the base space of a semi-universal deformation of rational quadruple points. Ann. Math. 134:653–678. DOI: 10.2307/2944359.
   Web of Science ®Google Scholar
• Komeda, J. (1994). On the existence of Weierstrass gap sequences on curves of genus ≤ 8. J. Pure Appl. Algebra 97:51–71. DOI: 10.1016/0022-4049(94)90039-6.
   Google Scholar
• Looijenga, E. (1984). The smoothing components of a triangle singularity. II. Math. Ann. 269:357–387. DOI: 10.1007/BF01450700.
   Web of Science ®Google Scholar
• Martin, B. (2020). Deform.lib. A Singular 4-1-3 library for computing Miniversal Deformation of Singularities and Modules.
   Google Scholar
• Nakano, T. (2008). On the moduli space of pointed algebraic curves of low genus II —rationality—. Tokyo J. Math. 31:147–160. DOI: 10.3836/tjm/1219844828.
   Google Scholar
• Nakano, T. (2016). On the moduli space of pointed algebraic curves of low genus III —positive characteristic—. Tokyo J. Math. 39:565–582. DOI: 10.3836/tjm/1484903137.
   Web of Science ®Google Scholar
• Nakano, T., Mori, T. (2004). On the moduli space of pointed algebraic curves of low genus: a computational approach. Tokyo J. Math. 27:239–253. DOI: 10.3836/tjm/1244208488.
   Google Scholar
• Pinkham, H. C. (1974). Deformations of algebraic varieties with Gm -action. Astérisque, Vol. 20. Paris, France: Société Mathématique de France, Paris, pp. 1–131.
   Google Scholar
• Rim, D. S., Vitulli, M. A. (1977). Weierstrass points and monomial curves. J. Algebra 48:454–476. DOI: 10.1016/0021-8693(77)90322-2.
   Web of Science ®Google Scholar
• Stevens, J. (1993). The versal deformation of universal curve singularities. Abh. Math. Sem. Univ. Hamburg 63:197–213. DOI: 10.1007/BF02941342.
   Web of Science ®Google Scholar
• Stevens, J. (2003). Deformations of Singularities, Lecture Notes in Mathematics, Vol. 1811. Berlin: Springer. DOI: 10.1007/b10723.
   Google Scholar
• Stevens, J. (2013). Computing versal deformations of singularities with Hauser’s algorithm. In: Deformations of Surface Singularities. Bolyai Society Mathematical Studies, Vol. 23. Berlin, Heidelberg: Springer, pp. 203–228. DOI: 10.1007/978-3-642-39131-6_6.
   Google Scholar