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Volume 23 Number 2 >

Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/578

Title: Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere
Authors: Rolf-Peter, Holzapfel
Keywords: Algebraic Curves
Abelian Threefolds
Period Matrices
Moduli Spaces
Shimura Surface
Siegel Domain
Complex Unit Ball
Uniformization
Braid Group
Monodromy Group
Modular Group
Gundamental Groups
Picard-Fuchsian Groups
Symplectic Group
Aritmetic Group
Representation
Quadratic Number Field
Issue Date: 1997
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Serdica Mathematical Journal, Vol. 23, No 2, (1997), 143p-164p
Abstract: We define Picard cycles on each smooth three-sheeted Galois cover C of the Riemann sphere. The moduli space of all these algebraic curves is a nice Shimura surface, namely a symmetric quotient of the projective plane uniformized by the complex two-dimensional unit ball. We show that all Picard cycles on C form a simple orbit of the Picard modular group of Eisenstein numbers. The proof uses a special surface classification in connection with the uniformization of a classical Picard-Fuchs system. It yields an explicit symplectic representation of the braid groups (coloured or not) of four strings.
URI: http://hdl.handle.net/10525/578
ISSN: 1310-6600
Appears in Collections:Volume 23 Number 2

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