## Journal of the Mathematical Society of Japan

### The diffeomorphic types of the complements of arrangements in $\bm{CP}^3$ I: Point arrangements

#### Abstract

For any arrangement of hyperplanes in $\bm{CP}^3$, we introduce the soul of this arrangement. The soul, which is a pseudo-complex, is determined by the combinatorics of the arrangement of hyperplanes. If the soul consists of a set of points (0-simplices) and a set of planes (2-simplices), then the arrangement is called point arrangement. In this paper, we give a sufficient combinatoric condition for two point arrangements of hyperplanes to be diffeomorphic to each other. In particular we have found sufficient condition on combinatorics for the point arrangement of hyperplanes whose moduli space is connected.

#### Article information

Source
J. Math. Soc. Japan, Volume 59, Number 2 (2007), 423-447.

Dates
First available in Project Euclid: 1 October 2007

https://projecteuclid.org/euclid.jmsj/1191247594

Digital Object Identifier
doi:10.2969/jmsj/05920423

Mathematical Reviews number (MathSciNet)
MR2325692

Zentralblatt MATH identifier
1140.14032

#### Citation

WANG, Shaobo; YAU, Stephen S.-T. The diffeomorphic types of the complements of arrangements in $\bm{CP}^3$ I: Point arrangements. J. Math. Soc. Japan 59 (2007), no. 2, 423--447. doi:10.2969/jmsj/05920423. https://projecteuclid.org/euclid.jmsj/1191247594

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