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 Cent. Eur. J. Math., 2012, Volume 10, Issue 2, Pages 521–529 (Mi cejm4)

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

F. Bogomolovab, Vik. S. Kulikovcb

a Courant Institute of Mathematical Sciences, New York University, 251 Mercer str., New York, NY 10012, USA
b Laboratory of Algebraic Geometry, GU-HSE, Vavilova Str. 7, Moscow, 117312, Russia
c Steklov Mathematical Institute, Gubkina Str. 8, Moscow, 119991, Russia

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 three 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].

 Funding Agency Grant Number National Science Foundation DMS-1001662 Ministry of Education and Science of the Russian Federation 11.G34.31.0023NSh-4713.2010.1 Russian Foundation for Basic Research 11-01-00185 The first author was supported by NSF grants DMS-1001662, both authors were supported by AG Laboratory HSE, RF government grant, ag. 11.G34.31.0023, and the second author was partially supported by grants of NSh-4713.2010.1 and RFBR 11-01-00185.

DOI: https://doi.org/10.2478/s11533-011-0116-x

Bibliographic databases:

Document Type: Article
MSC: 14N20, 52C35, 32S22