On the diffeomorphic type of the complement to a line arrangement in a projective plane

Fedor Bogomolov; Viktor S. Kulikov

doi:10.2478/s11533-011-0116-x

On the diffeomorphic type of the complement to a line arrangement in a projective plane

Fedor Bogomolov, Viktor S. Kulikov

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We show that the diffeomorphic type of the complement to a line arrangement in a complex projective plane P ² depends only on the graph of line intersections if no line in the arrangement contains more than two points in which at least two lines intersect. This result also holds for some special arrangements which do not satisfy this property. However it is not true in general, see [Rybnikov G., On the fundamental group of the complement of a complex hyperplane arrangement, Funct. Anal. Appl., 2011, 45(2), 137-148].

Original language	English (US)
Pages (from-to)	521-529
Number of pages	9
Journal	Central European Journal of Mathematics
Volume	10
Issue number	2
DOIs	https://doi.org/10.2478/s11533-011-0116-x
State	Published - Apr 2012

Keywords

Incidence matrix
Line arrangement

ASJC Scopus subject areas

General Mathematics

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10.2478/s11533-011-0116-x

Cite this

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abstract = "We show that the diffeomorphic type of the complement to a line arrangement in a complex projective plane P 2 depends only on the graph of line intersections if no line in the arrangement contains more than two points in which at least two lines intersect. This result also holds for some special arrangements which do not satisfy this property. However it is not true in general, see [Rybnikov G., On the fundamental group of the complement of a complex hyperplane arrangement, Funct. Anal. Appl., 2011, 45(2), 137-148].",

keywords = "Incidence matrix, Line arrangement",

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AB - We show that the diffeomorphic type of the complement to a line arrangement in a complex projective plane P 2 depends only on the graph of line intersections if no line in the arrangement contains more than two points in which at least two lines intersect. This result also holds for some special arrangements which do not satisfy this property. However it is not true in general, see [Rybnikov G., On the fundamental group of the complement of a complex hyperplane arrangement, Funct. Anal. Appl., 2011, 45(2), 137-148].

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On the diffeomorphic type of the complement to a line arrangement in a projective plane

Abstract

Keywords

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