On the diffeomorphic type of the complement to a line arrangement in a projective plane
- 65 Downloads
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].
KeywordsLine arrangement Incidence matrix
MSC14N20 52C35 32S22
Unable to display preview. Download preview PDF.
- Hirzebruch F., Arrangements of lines and algebraic surfaces, In: Arithmetic and Geometry II, Progr. Math., 36, Birkhäuser, Boston, 1983, 113–140Google Scholar