Algebraic curves with automorphism groups of large prime order

Arakelian, Nazar; Speziali, Pietro

doi:10.1007/s00209-021-02749-z

Cited by 3 publications

(2 citation statements)

References 18 publications

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“…The groups of orders 168, 360, 720, and 2520 are isomorphic to PSL(2, 7)), Alt 6 , Alt 6 • 2 and Alt 7 respectively. The groups of orders 216 and 72 are isomorphic to PGU(3, 2) and PSU (3,2), respectively, with the group of order 36 a subgroup of the latter.…”

Section: 2mentioning

confidence: 99%

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Plane curves with a large linear automorphism group in characteristic $p$

Borges¹,

Korchmáros²,

Speziali³

2022

Preprint

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Let G be a subgroup of the three dimensional projective group PGL(3, q) defined over a finite field Fq of order q, viewed as a subgroup of PGL(3, K) where K is an algebraic closure of Fq. For the seven nonsporadic, maximal subgroups G of PGL(3, q), we investigate the (projective, irreducible) plane curves defined over K that are left invariant by G. For each, we compute the minimum degree d(G) of Ginvariant curves, provide a classification of all G-invariant curves of degree d(G), and determine the first gap ε(G) in the spectrum of the degrees of all G-invariant curves. We show that the curves of degree d(G) belong to a pencil depending on G, unless they are uniquely determined by G. We also point out that G-invariant curves of degree d(G) have particular geometric features such as Frobenius nonclassicality and an unusual variation of the number of F q i -rational points. For most examples of plane curves left invariant by a large subgroup of PGL(3, q), the whole automorphism group of the curve is linear, i.e., a subgroup of PGL(3, K). Although this appears to be a general behavior, we show that the opposite case can also occur for some irreducible plane curves, that is, the curve has a large group of linear automorphisms, but its full automorphism group is nonlinear.

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Section: 2mentioning

confidence: 99%

“…If u = 5, then [3,Proposition 11] shows that U fixes two points on X and that X /U is elliptic. Assume that Aut(X ) has a unique tame short orbit.…”

Section: Nonclassicality Of G-invariant Irreducible Plane Curvesmentioning

confidence: 99%

Plane curves with a large linear automorphism group in characteristic $p$

Borges¹,

Korchmáros²,

Speziali³

2022

Preprint

View full text Add to dashboard Cite

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Plane curves with a large linear automorphism group in characteristic p

Borges,

Korchmáros,

Speziali

2024

Finite Fields and Their Applications

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On large prime actions on Riemann surfaces

Reyes-Carocca

Rojas

2022

Journal of Group Theory

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In this article, we study compact Riemann surfaces of genus 𝑔 with an automorphism of prime order g + 1 g+1 . The main result provides a classification of such surfaces. In addition, we give a description of them as algebraic curves, determine and realise their full automorphism groups and compute their fields of moduli. We also study some aspects of their Jacobian varieties such as isogeny decompositions and complex multiplication. Finally, we determine the period matrix of the Accola–Maclachlan curve of genus four.

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Algebraic curves with automorphism groups of large prime order

Cited by 3 publications

References 18 publications

Plane curves with a large linear automorphism group in characteristic $p$

Plane curves with a large linear automorphism group in characteristic $p$

Plane curves with a large linear automorphism group in characteristic p

On large prime actions on Riemann surfaces

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