The fundamental group of a Galois cover of ℂℙ1×T

• DOI: 10.2140/agt.2002.2.403
• Publication Date: 2005-06-15T13:10:33Z
• Authors: Meirav Amram; David Goldberg; Mina Teicher; Uzi Vishne
• Keywords: Mathematics - Algebraic Geometry; 14Q10, 14J99, 14J80, 32Q55; FOS: Mathematics; Algebraic Topology (math.AT); Mathematics - Algebraic Topology; 0101 mathematics; Algebraic Geometry (math.AG); 01 natural sciences

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-20.abs.html<br/>Let T be the complex projective torus, and X the surface CP^1 X T. 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^10.<br/>