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Fundamental groups of some special quadric arrangements. (English) Zbl 1109.14026

Rev. Mat. Complut. 19, No. 2, 259-276 (2006); erratum ibid. 22, No. 2, 517-550 (2009).
Summary: Continuing our work on the fundamental groups of conic-line arrangements [M. Amram, M. Teicher and M.A. Uludag, Topology Appl. 130, No. 2, 159–173 (2003; Zbl 1023.52008)], we obtain presentations of fundamental groups of the complements of three families of quadric arrangements in \(\mathbb{P}^2\). The first arrangement is a union of \(n\) conics, which are tangent to each other at two common points. The second arrangement is composed of \(n\) quadrics which are tangent to each other at one common point. The third arrangement is composed of \(n\) quadrics, \(n-1\) of them are tangent to the \(n\)-th one and each one of the \(n-1\) quadrics is transversal to the other \(n-2\) ones.

MSC:

14H20 Singularities of curves, local rings
14H30 Coverings of curves, fundamental group
14Q05 Computational aspects of algebraic curves

Citations:

Zbl 1023.52008
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