Open Access
April, 2007 The diffeomorphic types of the complements of arrangements in CP 3 I: Point arrangements
Shaobo WANG, Stephen S.-T. YAU
J. Math. Soc. Japan 59(2): 423-447 (April, 2007). DOI: 10.2969/jmsj/05920423


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.


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Shaobo WANG. Stephen S.-T. YAU. "The diffeomorphic types of the complements of arrangements in CP 3 I: Point arrangements." J. Math. Soc. Japan 59 (2) 423 - 447, April, 2007.


Published: April, 2007
First available in Project Euclid: 1 October 2007

zbMATH: 1140.14032
MathSciNet: MR2325692
Digital Object Identifier: 10.2969/jmsj/05920423

Primary: 14J15
Secondary: 52C35 , 57R50 , 68R05

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

Rights: Copyright © 2007 Mathematical Society of Japan

Vol.59 • No. 2 • April, 2007
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