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.
@article{bwmeta1.element.doi-10_1515_coma-2015-0009,
author = {Nobuhiro Honda},
title = {Geometry of some twistor spaces of algebraic dimension one},
journal = {Complex Manifolds},
volume = {2},
year = {2015},
zbl = {1326.32034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_coma-2015-0009}
}
Nobuhiro Honda. Geometry of some twistor spaces of algebraic dimension one. Complex Manifolds, Tome 2 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_coma-2015-0009/
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