Higher degree Galois covers of CP^1 x T

Details Higher degree Galois covers of CP^1 x T Higher degree Galois covers of CP^1 x T

2004-10-26

arxiv.org/abs/math/0410554v1

Algebr. Geom. Topol. 4 (2004) 841-859

Mathematics

Algebraic Geometry

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-37.abs.html

Scientific paper

Let T be a complex torus, and X the surface CP^1 x T. If T is embedded in CP^{n-1} then X may be embedded in CP^{2n-1}. Let X_Gal be its Galois cover with respect to a generic projection to CP^2. In this paper we compute the fundamental group of X_Gal, using the degeneration and regeneration techniques, the Moishezon-Teicher braid monodromy algorithm and group calculations. We show that pi_1(X_Gal) = Z^{4n-2}.

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