On fundamental groups related to the Hirzebruch surface F1

Michael Friedman*, Mina Teicher

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Given a projective surface and a generic projection to the plane, the braid monodromy factorization (and thus, the braid monodromy type) of the complement of its branch curve is one of the most important topological invariants, stable on deformations. From this factorization, one can compute the fundamental group of the complement of the branch curve, either in ℂ2 or in ℂℙ2. In this article, we show that these groups, for the Hirzebruch surface F 1,(a,b), are almost-solvable. That is, they are an extension of a solvable group, which strengthen the conjecture on degeneratable surfaces.

Original languageEnglish
Pages (from-to)728-745
Number of pages18
JournalScience in China, Series A: Mathematics
Volume51
Issue number4
DOIs
StatePublished - Apr 2008
Externally publishedYes

Funding

FundersFunder number
Israel Science Foundation8008/02-3

    Keywords

    • Braid monodromy
    • Branch curve
    • Classification of surfaces
    • Degeneration
    • Fundamental group
    • Generic projection
    • Hirzebruch surfaces

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