Fundamental groups of some quadric-line arrangements

2002/08/30 by Meirav Amram, Amram, Meirav, Mina Teicher +4
Engineering · Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems #math.AG

paper · pdf · doi:10.48550/arxiv.math/0208248

19 pages

arxiv created 2002/08/30 · openalex publication_date 2002/08/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we obtain presentations of fundamental groups of the complements of three quadric-line arrangements in P². The first arrangement is a smooth quadric Q with n tangent lines to Q, and the second one is a quadric Q with n lines passing through a point p not in Q. The last arrangement consists of a quadric Q with n lines passing through a point p in Q.

Related

• Fundamental groups of some special quadric arrangements
• On the fundamental group of the complement of two tangent conics and an arbitrary number of tangent lines
• Fundamental groups of Tangent Conic-Line arrangements with Singularities up to order 6
• On the connection between affine and projective fundamental groups of line arrangements and curves
• Common transversals and tangents to two lines and two quadrics in P³