Algebraic dimension of twistor spaces whose fundamental system is a pencil:

Nobuhiro Honda; Bernd Kreußler

doi:10.1112/jlms.12043

Algebraic dimension of twistor spaces whose fundamental system is a pencil:

Nobuhiro Honda, Bernd Kreußler

Mathematics & Computer Studies

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We show that the algebraic dimension of a twistor space over nCP2 cannot be two if n>4 and the fundamental system (that is, the linear system associated to the half-anti-canonical bundle, which is available on any twistor space) is a pencil. This means that if the algebraic dimension of a twistor space on nCP2, n>4, is two, then the fundamental system is either empty or consists of a single member. The existence problem for a twistor space on nCP2 with algebraic dimension two is open for n>4.

Original language	English
Pages (from-to)	989-1010
Number of pages	22
Journal	Journal of the London Mathematical Society
Volume	95
Issue number	3
DOIs	https://doi.org/10.1112/jlms.12043
Publication status	Published - 2017

Funding

Received 8 August 2016; revised 14 January 2017; published online 28 March 2017. 2010 Mathematics Subject Classification 53A30, 53C28 (primary). The first named author has been partially supported by JSPS KAKENHI (grant number 24540061).

Funders	Funder number
Japan Society for the Promotion of Science	15H02057, 16H03932, 24540061
Japan Society for the Promotion of Science

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10.1112/jlms.12043

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abstract = "We show that the algebraic dimension of a twistor space over nCP2 cannot be two if n>4 and the fundamental system (that is, the linear system associated to the half-anti-canonical bundle, which is available on any twistor space) is a pencil. This means that if the algebraic dimension of a twistor space on nCP2, n>4, is two, then the fundamental system is either empty or consists of a single member. The existence problem for a twistor space on nCP2 with algebraic dimension two is open for n>4.",

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AB - We show that the algebraic dimension of a twistor space over nCP2 cannot be two if n>4 and the fundamental system (that is, the linear system associated to the half-anti-canonical bundle, which is available on any twistor space) is a pencil. This means that if the algebraic dimension of a twistor space on nCP2, n>4, is two, then the fundamental system is either empty or consists of a single member. The existence problem for a twistor space on nCP2 with algebraic dimension two is open for n>4.

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Algebraic dimension of twistor spaces whose fundamental system is a pencil:

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