Algebraic and Geometric Topology 4 (2004), paper no. 37, pages 841-859.

Higher degree Galois covers of CP^1 x T

Meirav Amram, David Goldberg

Abstract. 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}.

Keywords. Galois cover, fundamental group, generic projection, Sieberg-Witten invariants

AMS subject classification. Primary: 14Q10. Secondary: 14J80, 32Q55.

DOI: 10.2140/agt.2004.4.841

E-print: arXiv:math.AG/0410554

Submitted: 17 June 2004. Accepted: 6 October 2004. Published: 7 October 2004.

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Meirav Amram, David Goldberg

Einstein Institute for Mathematics
The Hebrew University, Jerusalem, Israel

Mathematics Department, Colorado State University
Fort Collins, CO 80523 USA

Email: ameirav@math.huji.ac.il, david_j_goldberg@hotmail.com

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