an:05538191
Zbl 1174.53345
Brown, J. R.
Properties of a hypothetical exotic complex structure on \(\mathbb C\mathbb P^3\)
EN
Math. Bohem. 132, No. 1, 59-74 (2007).
00248098
2007
j
53C56 53C15 58J20 55T99
projective space; Fr??licher spectral sequence; Hodge numbers
Summary: We consider almost-complex structures on \(\mathbb C\mathbb P^3\) whose total Chern classes differ from that of the standard (integrable) almost-complex structure. \textit{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 Fr??licher spectral sequence at the second level.