The fundamental group of a Galois cover of ℂℙ1 × T

Let $T$ be the complex projective torus, and $X$ the surface ${ℂ ℙ}^{1} \times T$ . Let $X_{Gal}$ be its Galois cover with respect to a generic projection to ${ℂ ℙ}^{2}$ . 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 $π_{1} (X_{Gal}) = ℤ^{10}$ .

Keywords

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

Mathematical Subject Classification 2000

Primary: 14Q10, 14J99

Secondary: 14J80, 32Q55

References

Forward citations

Publication

Received: 15 March 2002

Revised: 9 May 2002

Accepted: 15 May 2002

Published: 25 May 2002

Authors

Meirav Amram
Department of Mathematics, Bar-Ilan University Ramat-Gan 52900 Israel

David Goldberg
Department of Mathematics Bar-Ilan University Ramat-Gan 52900 Israel

Mina Teicher
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

Volume 2, issue 1 (2002)

Meirav Amram, David Goldberg, Mina Teicher and Uzi Vishne