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Higher degree Galois covers of CP¹ × T

Meirav Amram and David Goldberg

Algebraic & Geometric Topology 4 (2004) 841–859

DOI: 10.2140/agt.2004.4.841

arXiv: math.AG/0410554
Abstract

Let T be a complex torus, and X the surface CP1 × T. If T is embedded in CPn-1 then X may be embedded in CP2n-1. Let XGal be its Galois cover with respect to a generic projection to CP2. 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) = Z4n-2.

Keywords

Galois cover, fundamental group, generic projection, Sieberg–Witten invariants
Mathematical Subject Classification

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