Journal of the Mathematical Society of Japan

The diffeomorphic types of the complements of arrangements in CP 3 I: Point arrangements

Shaobo WANG and Stephen S.-T. YAU

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For any arrangement of hyperplanes in 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

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

First available in Project Euclid: 1 October 2007

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Zentralblatt MATH identifier

Primary: 14J15: Moduli, classification: analytic theory; relations with modular forms [See also 32G13]
Secondary: 52C35: Arrangements of points, flats, hyperplanes [See also 32S22] 68R05: Combinatorics 57R50: Diffeomorphisms

arrangement moduli space hyperplane nice point arrangement combinatorics diffeomorphic type complement and $\bm{CP}^3$


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.

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