## Moishezon twistor spaces without effective divisors of degree one (pre-published version)

#### Citation

Kreussler, B. (1995) 'Moishezon twistor spaces without effective divisors of degree one.' Journal of Algebraic Geometry 6(1). pp. 1-17. DOI: 10.1.1.53.3627.

*Kreussler, B. (1995) 'Moishezon twistor spaces without effective divisors of degree one.' Journal of Algebraic Geometry 6(1). pp. 1-17. DOI: 10.1.1.53.3627.*

##### Abstract

We study simply connected compact twistor spaces Z of positive type. Assuming that the fundamental linear system j \Gamma 1 2 Kj is at least a pencil, we prove the following theorem: the existence of an irreducible curve C ae Z which is invariant under the real structure of Z and has the property C:(\Gamma 1 2 K) ! 0 implies that the twistor space is Moishezon but does not contain effective divisors of degree one. Furthermore, we prove the existence of such twistor spaces with arbitrary Picard number ae(Z) 5. These are the first examples of Moishezon twistor spaces without divisors of degree one.

##### Keywords

Degree oneArbitrary Picard number ae

Positive type

Moishezon twistor space

Fundamental linear system gamma

Effective divisor

Irreducible curve ae

Real structure

Compact twistor space

##### Language (ISO 639-3)

eng##### Publisher

Universität Kaiserslautern##### DOI

10.1.1.53.3627##### Collections

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