Article
MSC:
32J17,
53C15,
53C56,
55T99,
58A14,
58J20 | MR 2311754 | Zbl 1174.53345 | DOI: 10.21136/MB.2007.133989
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Keywords:
complex structure; projective space; Frölicher spectral sequence; Hodge numbers
complex structure; projective space; Frölicher spectral sequence; Hodge numbers
Summary:
We consider almost-complex structures on $\mathbb{C}\text{P}^3$ whose total Chern classes differ from that of the standard (integrable) almost-complex structure. E. Thomas established the existence of many such structures. We show that if there exists an “exotic” integrable almost-complex structures, then the resulting complex manifold would have specific Hodge numbers which do not vanish. We also give a necessary condition for the nondegeneration of the Frölicher spectral sequence at the second level.
References:
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