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- Title
THE FUNDAMENTAL GROUP OF THE GALOIS COVER OF HIRZEBRUCH SURFACE F<sub>1</sub>(2, 2).
- Authors
AMRAM, MEIRAV; TEICHER, MINA; VISHNE, UZI
- Abstract
This paper is the second in a series of papers concerning Hirzebruch surfaces. In the first paper in this series, the fundamental group of Galois covers of Hirzebruch surfaces Fk(a, b), where a, b are relatively prime, was shown to be trivial. For the general case, the conjecture stated that the fundamental group is $\mathbb{Z}_{c}^{n-2}$ where c = gcd(a, b) and n = 2ab + kb2. In this paper, we degenerate the Hirzebruch surface F1(2, 2), compute the braid monodromy factorization of the branch curve in ℂ2, and verify that, in this case, the conjecture holds: the fundamental group of the Galois cover of F1(2, 2) with respect to a generic projection is isomorphic to $\mathbb{Z}_2^{10}$.
- Subjects
GROUP theory; GALOIS theory; GEOMETRIC surfaces; MONODROMY groups; FACTORIZATION
- Publication
International Journal of Algebra & Computation, 2007, Vol 17, Issue 3, p507
- ISSN
0218-1967
- Publication type
Article
- DOI
10.1142/S0218196707003780