Geometry of some twistor spaces of algebraic dimension one

Nobuhiro Honda

Complex Manifolds (2015)

  • Volume: 2, Issue: 1, page 105-130, electronic only
  • ISSN: 2300-7443

Abstract

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It is shown that there exists a twistor space on the n-fold connected sum of complex projective planes nCP2, whose algebraic dimension is one and whose general fiber of the algebraic reduction is birational to an elliptic ruled surface or a K3 surface. The former kind of twistor spaces are constructed over nCP2 for any n ≥ 5, while the latter kind of example is constructed over 5CP2. Both of these seem to be the first such example on nCP2. The algebraic reduction in these examples is induced by the anti-canonical system of the twistor spaces. It is also shown that the former kind of twistor spaces contain a pair of non-normal Hopf surfaces.

How to cite

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Nobuhiro Honda. "Geometry of some twistor spaces of algebraic dimension one." Complex Manifolds 2.1 (2015): 105-130, electronic only. <http://eudml.org/doc/275894>.

@article{NobuhiroHonda2015,
abstract = {It is shown that there exists a twistor space on the n-fold connected sum of complex projective planes nCP2, whose algebraic dimension is one and whose general fiber of the algebraic reduction is birational to an elliptic ruled surface or a K3 surface. The former kind of twistor spaces are constructed over nCP2 for any n ≥ 5, while the latter kind of example is constructed over 5CP2. Both of these seem to be the first such example on nCP2. The algebraic reduction in these examples is induced by the anti-canonical system of the twistor spaces. It is also shown that the former kind of twistor spaces contain a pair of non-normal Hopf surfaces.},
author = {Nobuhiro Honda},
journal = {Complex Manifolds},
keywords = {twistor space; elliptic ruled surface; K3 surface},
language = {eng},
number = {1},
pages = {105-130, electronic only},
title = {Geometry of some twistor spaces of algebraic dimension one},
url = {http://eudml.org/doc/275894},
volume = {2},
year = {2015},
}

TY - JOUR
AU - Nobuhiro Honda
TI - Geometry of some twistor spaces of algebraic dimension one
JO - Complex Manifolds
PY - 2015
VL - 2
IS - 1
SP - 105
EP - 130, electronic only
AB - It is shown that there exists a twistor space on the n-fold connected sum of complex projective planes nCP2, whose algebraic dimension is one and whose general fiber of the algebraic reduction is birational to an elliptic ruled surface or a K3 surface. The former kind of twistor spaces are constructed over nCP2 for any n ≥ 5, while the latter kind of example is constructed over 5CP2. Both of these seem to be the first such example on nCP2. The algebraic reduction in these examples is induced by the anti-canonical system of the twistor spaces. It is also shown that the former kind of twistor spaces contain a pair of non-normal Hopf surfaces.
LA - eng
KW - twistor space; elliptic ruled surface; K3 surface
UR - http://eudml.org/doc/275894
ER -

References

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