一个𝔽p2-maximal女人的性别及其自同构

IF 0.5 4区数学 Q3 MATHEMATICS

Advances in Geometry Pub Date : 2021-10-01 DOI:10.1515/advgeom-2020-0012

M. Giulietti, M. Kawakita, Stefano Lia, M. Montanucci

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引用次数: 0

摘要

摘要1895年Wiman引入了黎曼曲面𝒲 复数域上的属6ℂ 由方程X6+Y6定义+ℨ6+（X2+Y2+ℨ2）（X4+Y4+ℨ4） −12X2Y2ℨ2＝0，并证明了它的全自同构群同构于对称群S5。我们证明了这也适用于所有代数闭域𝕂 特征p≥7。对于p＝2，3，上述多项式在𝕂, 对于p=5，曲线𝒲 是理性和自闭症(𝒲) ≅ PGL（2，𝕂). 我们还展示了Wiman𝔽192最大性感𝒲 不是Galois被有限域上的Hermitian曲线H19覆盖𝔽192

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An 𝔽p2-maximal Wiman sextic and its automorphisms

Abstract In 1895 Wiman introduced the Riemann surface 𝒲 of genus 6 over the complex field ℂ defined by the equation X6+Y6+ℨ6+(X2+Y2+ℨ2)(X4+Y4+ℨ4)−12X2Y2ℨ2 = 0, and showed that its full automorphism group is isomorphic to the symmetric group S5. We show that this holds also over every algebraically closed field 𝕂 of characteristic p ≥ 7. For p = 2, 3 the above polynomial is reducible over 𝕂, and for p = 5 the curve 𝒲 is rational and Aut(𝒲) ≅ PGL(2,𝕂). We also show that Wiman’s 𝔽192-maximal sextic 𝒲 is not Galois covered by the Hermitian curve H19 over the finite field 𝔽192.

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来源期刊

Advances in Geometry 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.