#### 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.

Notes on file formats
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

AGT home page

## Archival Version

**These pages are not updated anymore.
They reflect the state of
.
For the current production of this journal, please refer to
http://msp.warwick.ac.uk/.
**