Geometry of some twistor spaces of algebraic dimension one

• Autorzy: Nobuhiro Honda
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 53A30: Conformal differential geometry

• Wydawca: De Gruyter Open
• Czasopismo: Complex Manifolds
• Rocznik: 2015
• Tom: 2
• Numer: 1

Daty

otrzymano

2015-06-02

zaakceptowano

2015-08-29

online

2015-09-09

Twórcy

autor

Nobuhiro Honda

• Department of Mathematics, Tokyo Institute of Technology

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• ---
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Identyfikatory

DOI

10.1515/coma-2015-0009