Quasiplatonic curves with symmetry group Z22⋊Zm are definable over Q

Hidalgo, Rubén A.; Jiménez, Leslie; Quispe, Saúl; Reyes-Carocca, Sebastián

doi:10.1112/blms.12014

Cited by 17 publications

(7 citation statements)

References 13 publications

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“…The decomposition of Jacobians with group actions has been extensively studied; the simplest case of such a decomposition was already noticed by Wirtinger in [45] and used by Schottky and Jung in [39]. For decompositions of Jacobians with respect to special groups, we refer to [9,18,20,31,32,36].…”

Section: Preliminariesmentioning

confidence: 99%

A note on large automorphism groups of compact Riemann surfaces

Izquierdo

Reyes-Carocca

2020

Journal of Algebra

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Belolipetsky and Jones classified those compact Riemann surfaces of genus g admitting a large group of automorphisms of order λ(g − 1), for each λ > 6, under the assumption that g − 1 is a prime number. In this article we study the remaining large cases; namely, we classify Riemann surfaces admitting 5(g − 1) and 6(g − 1) automorphisms, with g − 1 a prime number. As a consequence, we obtain the classification of Riemann surfaces admitting a group of automorphisms of order 3(g − 1), with g − 1 a prime number. We also provide isogeny decompositions of their Jacobian varieties.

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Section: Preliminariesmentioning

confidence: 99%

A note on large automorphism groups of compact Riemann surfaces

Izquierdo

Reyes-Carocca

2020

Journal of Algebra

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“…The simplest case of such a decomposition is when G is a group of order two; this fact was already noticed in 1895 by Wirtinger [37] and used by Schottky and Jung in [35]. For other special groups see, for example, [4,15,20,21,27,30,31,33]. In [22], Kani and Rosen studied relations among idempotents in the algebra of rational endomorphisms of an arbitrary abelian variety.…”

Section: Isogenous Decomposition Of the Jacobian Variety Of Fiber Pro...mentioning

confidence: 99%

On the fiber product of Riemann surfaces

Hidalgo¹,

Reyes-Carocca²,

Vega³

2016

Preprint

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Let S 0 , S 1 and S 2 be connected Riemann surfaces and let β 1 : S 1 → S 0 and β 2 : S 2 → S 0 be surjective holomorphic maps. The associated fiber product S 1 × (β 1 ,β 2 ) S 2 has the structure of a singular Riemann surface, endowed with a canonical map β to S 0 satisfying that β j • π j = β, where π j is coordinate projection onto S j . In this paper we provide a Fuchsian description of the fiber product and obtain that if one the maps β j is a regular branched cover, then all its irreducible components are isomorphic. In the case that both β j are of finite degree, we observe that the number of irreducible components is bounded above by the greatest common divisor of the two degrees; we study the irreducibility of the fiber product. In the case that S 0 = C, and S 1 and S 2 are compact, we define the strong field of moduli of the pair (S 1 × (β 1 ,β 2 ) S 2 , β) and observe that this field coincides with the minimal field containing the fields of moduli of both pairs (S 1 , β 1 ) and (S 2 , β 2 ). Finally, in the case that the fiber product is a connected Riemann surface, we provide an isogenous decomposition of its Jacobian variety.

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“…This decomposition of Jacobians under group actions has been extensively studied, following early papers by Wirtinger [51] and Schottky and Jung [45]. For decomposition of Jacobians with respect to specific groups, see [6,18,22,23,35,37,38,40,41].…”

Section: The Surfaces In Case (Xii) Havementioning

confidence: 99%

Groups of automorphisms of Riemann surfaces and maps of genus p + 1 where p is prime

2021

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We classify compact Riemann surfaces of genus g, where g − 1 is a prime p, which have a group of automorphisms of order ρ(g − 1) for some integer ρ ≥ 1, and determine isogeny decompositions of the corresponding Jacobian varieties. This extends results of Belolipetzky and the second author for ρ > 6, and of the first and third authors for ρ = 3, 4, 5 and 6. As a corollary we classify the orientably regular hypermaps (including maps) of genus p + 1, together with the non-orientable regular hypermaps of characteristic −p, with automorphism group of order divisible by the prime p; this extends results of Conder, Širáň and Tucker for maps.

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Quasiplatonic curves with symmetry group Z22⋊Zm are definable over Q

Cited by 17 publications

References 13 publications

A note on large automorphism groups of compact Riemann surfaces

A note on large automorphism groups of compact Riemann surfaces

On the fiber product of Riemann surfaces

Groups of automorphisms of Riemann surfaces and maps of genus p + 1 where p is prime

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