MATHEMATICA BOHEMICA, Vol. 132, No. 1, pp. 59-74 (2007)

Properties of a hypothetical exotic complex structure on $\Bbb C P^3$

J. R. Brown

J. Ryan Brown, Georgia College & State University, Department of Mathematics, CBX 017, Milledgeville, GA 31061, USA, e-mail:

Abstract: 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.

Keywords: complex structure, projective space, Frölicher spectral sequence, Hodge numbers

Classification (MSC2000): 53C56, 53C15, 58J20, 55T99

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