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Diffeomorphic types of complements of nice point arrangements in CPl

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Abstract

We use a new method to study arrangement in CP l, define a class of nice point arrangements and show that if two nice point arrangements have the same combinatorics, then their complements are diffeomorphic to each other. In particular, the moduli space of nice point arrangements with same combinatorics in CP l is connected. It generalizes the result on point arrangements in CP 3 to point arrangements in CP l for any l.

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Author information

Correspondence to Stephen S.-T. Yau.

Additional information

Dedicated to Prof. ZHONG TongDe on the occasion of his 80th birthday

This work was partially supported by National Natural Science Foundation of China (Grant No. 10731030) and Program of Shanghai Subject Chief Scientist (PSSCS) of Shanghai

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Yau, S.S., Ye, F. Diffeomorphic types of complements of nice point arrangements in CPl . Sci. China Ser. A-Math. 52, 2774 (2009). https://doi.org/10.1007/s11425-009-0202-8

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Keywords

  • diffeomorphic type
  • hyperplane arrangement
  • lattice isotopy

MSC(2000)

  • 14F05
  • 14H30