Algebraic curves with automorphism groups of large prime order

Autor(es)

Arakelian, Nazar ^[1] ; Speziali, Pietro ^[2]

Afiliação do(s) autor(es)

^[1] Univ Fed ABC, Ctr Matemat Comp & Cognicao, BR-09210580 Santo Andre, SP - Brazil

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: MATHEMATISCHE ZEITSCHRIFT; v. 299, n. 3-4, p. 2005-2028, DEC 2021.
• Citações Web of Science: 0

Resumo

Let X be a (projective, algebraic, non-singular, absolutely irreducible) curve of genus g defined over an algebraically closed field K of characteristic p >= 0, and let q be a prime dividing the cardinality of Aut(X). We say that X is a q-curve. Homma proved that either q <= 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. (AU)

• Processo FAPESP: 17/18776-6 - Curvas algébricas em característica positiva e aplicações
• Beneficiário: Pietro Speziali
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado