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

Fedor Bogomolov; Viktor Kulikov

Open Mathematics (2012)

  • Volume: 10, Issue: 2, page 521-529
  • ISSN: 2391-5455

Abstract

top
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].

How to cite

top

Fedor Bogomolov, and Viktor Kulikov. "On the diffeomorphic type of the complement to a line arrangement in a projective plane." Open Mathematics 10.2 (2012): 521-529. <http://eudml.org/doc/269038>.

@article{FedorBogomolov2012,
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].},
author = {Fedor Bogomolov, Viktor Kulikov},
journal = {Open Mathematics},
keywords = {Line arrangement; Incidence matrix; line arrangement; incidence matrix},
language = {eng},
number = {2},
pages = {521-529},
title = {On the diffeomorphic type of the complement to a line arrangement in a projective plane},
url = {http://eudml.org/doc/269038},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Fedor Bogomolov
AU - Viktor Kulikov
TI - On the diffeomorphic type of the complement to a line arrangement in a projective plane
JO - Open Mathematics
PY - 2012
VL - 10
IS - 2
SP - 521
EP - 529
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].
LA - eng
KW - Line arrangement; Incidence matrix; line arrangement; incidence matrix
UR - http://eudml.org/doc/269038
ER -

References

top
  1. [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 Zbl1205.14034
  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 Zbl0911.14007
  3. [3] Hirzebruch F., Arrangements of lines and algebraic surfaces, In: Arithmetic and Geometry II, Progr. Math., 36, Birkhäuser, Boston, 1983, 113–140 
  4. [4] Jiang T., Yau S.S.-T., Diffeomorphic types of the complements of arrangements of hyperplanes, Compositio Math., 1994, 92(2), 133–155 Zbl0828.57018
  5. [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 Zbl1271.14085
  6. [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 Zbl1115.52010

NotesEmbed ?

top

You must be logged in to post comments.