Fundamental groups of some special quadric arrangements

Details Fundamental groups of some special quadric arrangements Fundamental groups of some special quadric arrangements

2006-01-18

arxiv.org/abs/math/0601454v3

Mathematics

Algebraic Geometry

21 pages, 12 main figures, appears in Revista Mathematicae

Scientific paper

In this work 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 $n$ quadrics, 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.

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