Geodesic
Higher degree Galois covers of ℂℙ1 ×T
Amram, Meirav1 ; Goldberg, David2
1Einstein Institute for Mathematics, The Hebrew University, Jerusalem, Israel
2Mathematics Department, Colorado State University, Fort Collins CO 80523, USA
Algebraic and Geometric Topology, Tome 4 (2004) no. 2, pp. 841-859
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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.

DOI : 10.2140/agt.2004.4.841
Keywords: Galois cover, fundamental group, generic projection, Sieberg–Witten invariants

Amram, Meirav  1   ; Goldberg, David  2

1 Einstein Institute for Mathematics, The Hebrew University, Jerusalem, Israel
2 Mathematics Department, Colorado State University, Fort Collins CO 80523, USA 
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Amram, Meirav; Goldberg, David. Higher degree Galois covers of ℂℙ1 ×T. Algebraic and Geometric Topology, Tome 4 (2004) no. 2, pp. 841-859. doi: 10.2140/agt.2004.4.841

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[4] B Moishezon, M Teicher, Braid group techniques in complex geometry IV: Braid monodromy of the branch curve $S_3$ of $V_3\rightarrow\mathbb{C}\mathrm{P}^2$ and application to $\pi_1(\mathbb{C}\mathrm{P}^2-S_3,*)$, from: "Classification of algebraic varieties (L'Aquila, 1992)", Contemp. Math. 162, Amer. Math. Soc. (1994) 333

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