# Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere

Serdica Mathematical Journal (1997)

- Volume: 23, Issue: 2, page 143-164
- ISSN: 1310-6600

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topRolf-Peter, Holzapfel. "Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere." Serdica Mathematical Journal 23.2 (1997): 143-164. <http://eudml.org/doc/11609>.

@article{Rolf1997,

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.},

author = {Rolf-Peter, Holzapfel},

journal = {Serdica Mathematical Journal},

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; Shimura surface; Siegel domain; complex unit ball; braid group; modular group; Picard-Fuchsian groups; quadratic number field},

language = {eng},

number = {2},

pages = {143-164},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere},

url = {http://eudml.org/doc/11609},

volume = {23},

year = {1997},

}

TY - JOUR

AU - Rolf-Peter, Holzapfel

TI - Symplectic Representation of a Braid Group on 3-Sheeted Covers of the Riemann Sphere

JO - Serdica Mathematical Journal

PY - 1997

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 23

IS - 2

SP - 143

EP - 164

AB - 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.

LA - eng

KW - 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; Shimura surface; Siegel domain; complex unit ball; braid group; modular group; Picard-Fuchsian groups; quadratic number field

UR - http://eudml.org/doc/11609

ER -

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