Automorphism groups of non-singular plane curves of degree 5
Badr, Eslam (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Bars Cortina, Francesc (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2016
Abstract:	Let Mg be the moduli space of smooth, genus g curves over an algebraically closed field K of zero characteristic. Denote by Mg(G) the subset of Mg of curves δ such that G (as a finite nontrivial group) is isomorphic to a subgroup of Aut(δ), and let Mg(G) be the subset of curves δ such that G ≅ Aut(δ), where Aut(δ) is the full automorphism group of δ. Now, for an integer d ≥ 4, let MgPl be the subset of Mg representing smooth, genus g, plane curves of degree d, i. e. smooth curves that admits a plane non-singular model of degree d, (in this case, g = (d − 1)(d − 2)/2), and consider the sets MgPl (G):= MgPl ∩ Mg (G)and MgPl (G):= Mg (G) ∩ MgPl. Henn in [7] and Komiya and Kuribayashi in [10], listed the groups G for which M3Pl (G) is nonempty. In this article, we determine the loci M6Pl (G), corresponding to nonsingular degree 5 projective plane curves, which are nonempty. Also, we present the analogy of Henn's results for quartic curves concerning nonsingular plane model equations associated to these loci (see Table 2 for more details). Similar arguments can be applied to deal with higher degrees.
Grants:	Ministerio de Economía y Competitividad MTM2013-40680-P
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió sotmesa a revisió
Subject:	Plane curves ; Automorphism groups
Published in:	Communications in Algebra, Vol. 44, Issue 10 (June 2016) , p. 4327-4340, ISSN 1532-4125

DOI: 10.1080/00927872.2015.1087547

Preprint 12 p, 278.8 KB

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