# 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

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topFedor 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] 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] 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] 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 Zbl0828.57018
- [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] 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

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