Geodesic
Properties of a hypothetical exotic complex structure on $\Bbb C{\rm P}\sp 3$
Mathematica Bohemica, Tome 132 (2007) no. 1, pp. 59-74

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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.
DOI : 10.21136/MB.2007.133989
Classification : 32J17, 53C15, 53C56, 55T99, 58A14, 58J20
Keywords: complex structure; projective space; Frölicher spectral sequence; Hodge numbers 
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Brown, J. R. Properties of a hypothetical exotic complex structure on $\Bbb C{\rm P}\sp 3$. Mathematica Bohemica, Tome 132 (2007) no. 1, pp. 59-74. doi: 10.21136/MB.2007.133989

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