Volume 4, issue 2 (2004)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Higher degree Galois covers of $\mathbb{CP}^1 \times T$

Meirav Amram and David Goldberg

Algebraic & Geometric Topology 4 (2004) 841–859

arXiv: math.AG/0410554

Abstract

Let T be a complex torus, and X the surface 1 × T. If T is embedded in n1 then X may be embedded in 2n1. Let XGal be its Galois cover with respect to a generic projection to 2. In this paper we compute the fundamental group of XGal, using the degeneration and regeneration techniques, the Moishezon–Teicher braid monodromy algorithm and group calculations. We show that π1(XGal) = 4n2.

Keywords
Galois cover, fundamental group, generic projection, Sieberg–Witten invariants
Mathematical Subject Classification 2000
Primary: 14Q10
Secondary: 14J80, 32Q55
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Publication
Received: 17 June 2004
Accepted: 6 October 2004
Published: 7 October 2004
Authors
Meirav Amram
Einstein Institute for Mathematics
The Hebrew University
Jerusalem
Israel
David Goldberg
Mathematics Department
Colorado State University
Fort Collins CO 80523
USA