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Schottky Uniformizations of Genus 3 and 4 Reflecting S 4
Author(s) -
Hidalgo Rubén A.
Publication year - 2005
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610705006617
Subject(s) - automorphism , genus , riemann surface , abelian group , group (periodic table) , dimension (graph theory) , mathematics , conformal map , product (mathematics) , schottky diode , symplectic geometry , pure mathematics , symplectic group , mathematical analysis , physics , geometry , quantum mechanics , botany , diode , biology
Schottky uniformizations are provided of every closed Riemann surface S of genus g ∈ {3,4} admitting the symmetric group S 4 as group of conformal automorphisms. These Schottky uniformizations reflect the group S 4 and permit concrete representations of S 4 to be obtained in the respective symplectic group Sp g (Z). Their corresponding fixed points, in the Siegel space, give principally polarized Abelian varieties of dimension g . For g = 3 and for some cases of g = 4 they turn out to be holomorphically equivalent to the product of elliptic curves.