Algebraic and Geometric Topology 2 (2002), paper no. 20, pages 403-432.

The fundamental group of a Galois cover of CP^1 X T

Meirav Amram, David Goldberg, Mina Teicher, Uzi Vishne

Abstract. 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.

Keywords. Galois cover, fundamental group, generic projection, Moishezon-Teicher braid monodromy algorithm, Sieberg-Witten invariants

AMS subject classification. Primary: 14Q10, 14J99. Secondary: 14J80, 12F10.

DOI: 10.2140/agt.2002.2.403

E-print: arXiv:math.AG/0205272

Submitted: 15 March 2002. (Revised: 9 May 2002.) Accepted: 15 May 2002. Published: 25 May 2002.

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Meirav Amram and Mina Teicher:
Department of Mathematics, Bar-Ilan University, Ramat-Gan 52900, Israel

David Goldberg:
Department of Mathematics, Colorado State University
Fort Collins, CO 80523-1874, USA

Uzi Vishne:
Einstein Institute of Mathematics, Givat Ram Campus
The Hebrew University of Jerusalem, Jerusalem 91904, Israel

Emails: amram@mi.uni-erlangen.de, meirav@macs.biu.ac.il, goldberg@math.colostate.edu, teicher@macs.biu.ac.il, vishne@math.huji.ac.il

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