Automorphism Groups of Nonsingular Plane Curves of Degree 5

Eslam Badr, Francesc Bars

Research output: Contribution to journalArticleResearchpeer-review

5 Citations (Scopus)

Abstract

© 2016, Copyright © Taylor & Francis Group, LLC. 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 (Formula presented.) 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 (Formula presented.). Henn in [7] and Komiya and Kuribayashi in [10], listed the groups G for which (Formula presented.) is nonempty. In this article, we determine the loci (Formula presented.) , 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.
Original languageEnglish
Pages (from-to)4327-4340
JournalCommunications in Algebra
Volume44
Issue number10
DOIs
Publication statusPublished - 2 Oct 2016

Keywords

  • Automorphism groups
  • Plane curves

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