Non-singular plane curves with an element of 'large' order in its automorphism group
| Autor: | Eslam Badr, Francesc Bars |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Degree (graph theory)
Group (mathematics) Plane curve Computer Science::Information Retrieval General Mathematics 010102 general mathematics Astrophysics::Instrumentation and Methods for Astrophysics Computer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing) Cyclic group 010103 numerical & computational mathematics 01 natural sciences Combinatorics TheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGES Integer Genus (mathematics) ComputingMethodologies_DOCUMENTANDTEXTPROCESSING Computer Science::General Literature Order (group theory) 0101 mathematics Algebraically closed field ComputingMilieux_MISCELLANEOUS Mathematics |
| Zdroj: | International Journal of Algebra and Computation. 26:399-433 |
| ISSN: | 1793-6500 0218-1967 |
| DOI: | 10.1142/s0218196716500168 |
| Popis: | Let [Formula: see text] be the moduli space of smooth, genus [Formula: see text] curves over an algebraically closed field [Formula: see text] of zero characteristic. Denote by [Formula: see text] the subset of [Formula: see text] of curves [Formula: see text] such that [Formula: see text] (as a finite nontrivial group) is isomorphic to a subgroup of [Formula: see text] and let [Formula: see text] be the subset of curves [Formula: see text] such that [Formula: see text], where [Formula: see text] is the full automorphism group of [Formula: see text]. Now, for an integer [Formula: see text], let [Formula: see text] be the subset of [Formula: see text] representing smooth, genus [Formula: see text] curves that admit a non-singular plane model of degree [Formula: see text] (in this case, [Formula: see text]) and consider the sets [Formula: see text] and [Formula: see text]. In this paper we first determine, for an arbitrary but a fixed degree [Formula: see text], an algorithm to list the possible values [Formula: see text] for which [Formula: see text] is non-empty, where [Formula: see text] denotes the cyclic group of order [Formula: see text]. In particular, we prove that [Formula: see text] should divide one of the integers: [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] or [Formula: see text]. Secondly, consider a curve [Formula: see text] with [Formula: see text] such that [Formula: see text] has an element of “very large” order, in the sense that this element is of order [Formula: see text], [Formula: see text], [Formula: see text] or [Formula: see text]. Then we investigate the groups [Formula: see text] for which [Formula: see text] and also we determine the locus [Formula: see text] in these situations. Moreover, we work with the same question when [Formula: see text] has an element of “large” order: [Formula: see text], [Formula: see text] or [Formula: see text] with [Formula: see text] an integer. |
| Databáze: | OpenAIRE |
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