Properties of a hypothetical exotic complex structure on 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 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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  9. Global nondeformability of the complex projective space Proceedings of the 1989 Taniguchi International Symposium on “Prospect in Complex Geometry” in Katata, Japan, Lecture Notes Math, vol. 1468, Springer, Berlin, 1991, pp. 254–280. (1991) MR1123546
  10. Complex structures on real vector bundles, Amer. J. Math. 89 (1967), 887–908. (1967) Zbl0174.54802MR0220310
  11. Hodge numbers of a hypothetical complex structure on the six sphere, Geom. Dedicata 81 (2000), 173–179. (2000) Zbl0996.53046MR1772200
  12. Calabi’s conjecture and some new results in algebraic geometry, Proc. Nat. Acad. Sci. USA 74 (1977), 1798–1799. (1977) Zbl0355.32028MR0451180

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