The fundamental group of the galois cover of Hirzebruch surface F 1 (2, 2)

Meirav Amram, Mina Teicher, Uzi Vishne

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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 ℤcn-2 where c = gcd(a, b) and n = 2ab + kb2. In this paper, we degenerate the Hirzebruch surface Fi(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 ℤ210.

Original languageEnglish
Pages (from-to)507-525
Number of pages19
JournalInternational Journal of Algebra and Computation
Volume17
Issue number3
DOIs
StatePublished - May 2007

Bibliographical note

Funding Information:
author is partially supported by the Emmy Noether Research Institute for Mathematics and the Minerva Foundation of Germany, and an Israel Science Foundation grant #8008/02-3 (Excellency Center “Group Theoretic Methods in the Study of Algebraic Varieties”), and by the Edmund Landau Center for Research in Mathematical Analysis and Related Areas, sponsored by the Minerva Foundation (Germany).

Keywords

  • Fundamental group of complement of branch curve
  • Galois cover
  • Hirzebruch surfaces

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