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

• Autorzy: Fedor Bogomolov , Viktor Kulikov
• Języki publikacji: EN

Abstrakty

EN

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].

Słowa kluczowe

EN

Line arrangement; Incidence matrix

Kategorie tematyczne

• 52C35: Arrangements of points, flats, hyperplanes
• 14N20: Configurations and arrangements of linear subspaces
• 32S22: Relations with arrangements of hyperplanes

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 2
• Strony: 521-529

Daty

wydano

2012-04-01

online

2012-01-18

Twórcy

autor

Fedor Bogomolov

autor

Viktor Kulikov

Bibliografia

• [1] Eliyahu M., Garber D., Teicher M., A conjugation-free geometric presentation of fundamental groups of arrangements, Manuscripta Math., 2010, 133(1–2), 247–271 http://dx.doi.org/10.1007/s00229-010-0380-2
• [2] Fan K.-M., Direct product of free groups as the fundamental group of the complement of a union of lines, Michigan Math. J., 1997, 44(2), 283–291 http://dx.doi.org/10.1307/mmj/1029005704
• [3] Hirzebruch F., Arrangements of lines and algebraic surfaces, In: Arithmetic and Geometry II, Progr. Math., 36, Birkhäuser, Boston, 1983, 113–140
• [4] Jiang T., Yau S.S.-T., Diffeomorphic types of the complements of arrangements of hyperplanes, Compositio Math., 1994, 92(2), 133–155
• [5] Rybnikov G., On the fundamental group of the complement of a complex hyperplane arrangement, Funct. Anal. Appl., 2011, 45(2), 137–148 http://dx.doi.org/10.1007/s10688-011-0015-8
• [6] Wang S., Yau S.S.-T., Rigidity of differentiable structure for new class of line arrangements, Comm. Anal. Geom., 2005, 13(5), 1057–1075

Identyfikatory

DOI

10.2478/s11533-011-0116-x