Properties of a hypothetical exotic complex structure on ℂ P 3

J. R. Brown

Mathematica Bohemica (2007)

  • Volume: 132, Issue: 1, page 59-74
  • ISSN: 0862-7959

Abstract

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We consider almost-complex structures on ℂ 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.

How to cite

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Brown, J. R.. "Properties of a hypothetical exotic complex structure on $\mathbb {C}{\rm P}^3$." Mathematica Bohemica 132.1 (2007): 59-74. <http://eudml.org/doc/250245>.

@article{Brown2007,
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.},
author = {Brown, J. R.},
journal = {Mathematica Bohemica},
keywords = {complex structure; projective space; Frölicher spectral sequence; Hodge numbers; projective space; Frölicher spectral sequence; Hodge numbers},
language = {eng},
number = {1},
pages = {59-74},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Properties of a hypothetical exotic complex structure on $\mathbb \{C\}\{\rm P\}^3$},
url = {http://eudml.org/doc/250245},
volume = {132},
year = {2007},
}

TY - JOUR
AU - Brown, J. R.
TI - Properties of a hypothetical exotic complex structure on $\mathbb {C}{\rm P}^3$
JO - Mathematica Bohemica
PY - 2007
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 132
IS - 1
SP - 59
EP - 74
AB - 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.
LA - eng
KW - complex structure; projective space; Frölicher spectral sequence; Hodge numbers; projective space; Frölicher spectral sequence; Hodge numbers
UR - http://eudml.org/doc/250245
ER -

References

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