Algebraic curves with automorphism groups of large prime order
| Autor: | Nazar Arakelian, Pietro Speziali |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Absolutely irreducible
FUNÇÕES AUTOMORFAS General Mathematics 010102 general mathematics Automorphism 01 natural sciences Prime (order theory) Combinatorics Mathematics - Algebraic Geometry Genus (mathematics) 0103 physical sciences FOS: Mathematics 010307 mathematical physics Classification of finite simple groups Algebraic curve 0101 mathematics Algebraically closed field Abelian group Algebraic Geometry (math.AG) Mathematics |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| Popis: | Let $${\mathcal {X}}$$ be a (projective, algebraic, non-singular, absolutely irreducible) curve of genus g defined over an algebraically closed field K of characteristic $$p \ge 0$$ , and let q be a prime dividing the cardinality of $$\text{ Aut }({\mathcal {X}})$$ . We say that $${\mathcal {X}}$$ is a q-curve. Homma proved that either $$q \le g+1$$ or $$q = 2g+1$$ , and classified $$(2g+1)$$ -curves up to birational equivalence. In this note, we give the analogous classification for $$(g+1)$$ -curves, including a characterization of hyperelliptic $$(g+1)$$ -curves. Also, we provide the characterization of the full automorphism groups of q-curves for $$q= 2g+1, g+1$$ . Here, we make use of two different techniques: the former case is handled via a result by Vdovin bounding the size of abelian subgroups of finite simple groups, the second via the classification by Giulietti and Korchmaros of automorphism groups of curves of even genus. Finally, we give some partial results on the classification of q-curves for $$q = g, g-1$$ . |
| Databáze: | OpenAIRE |
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