Higher degree Galois covers of \(\mathbb {CP}^1 \times T\). (English) Zbl 1069.14065
Let \(T\) be a complex torus, and \(X\) the surface \(\mathbb{C}\mathbb{P}^1\times T\). If \(T\) is embedded in \(\mathbb{C}\mathbb{P}^{n-1}\) then \(X\) may be embedded in \(\mathbb{C}\mathbb{P}^{2n-1}\). Let \(X_{\text{Gal}}\) be its Galois cover with respect to a generic projection to \(\mathbb{C}\mathbb{P}^2\). In this paper the fundamental group of \(X_{\text{Gal}}\) is computed, using the Moishezon-Teicher degeneration, regeneration and the braid monodromy algorithm. It is shown that \(\pi_1(X_{\text{Gal}})= \mathbb{Z}^{4n-2}\). This is a generalization of the results of
M. Amram, D. Goldberg, M. Teicher and U. Vishne [Algebr. Geom. Topol. 2, 403–432 (2002; Zbl 1037.14006)], where the case \(n=3\) was treated.
Reviewer: Mina Teicher (Ramat Gan)
MSC:
| 14Q10 | Computational aspects of algebraic surfaces |
| 14J80 | Topology of surfaces (Donaldson polynomials, Seiberg-Witten invariants) |
| 32Q55 | Topological aspects of complex manifolds |
Citations:
Zbl 1037.14006References:
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