On pluri-half-anticanonical systems of LeBrun twistor spaces

Author:
Nobuhiro Honda

Journal:
Proc. Amer. Math. Soc. **138** (2010), 2051-2060

MSC (2010):
Primary 32L25; Secondary 53C28

Published electronically:
December 8, 2009

MathSciNet review:
2596041

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Abstract: In this paper, we investigate pluri-half-anticanonical systems on the so-called LeBrun twistor spaces. We determine its dimension, the base locus, the structure of the associated rational map, and also the structure of general members, in precise form. In particular, we show that if and , the base locus of the system on consists of two non-singular rational curves, along which any member has singularity, and that if we blow up these curves, then the strict transform of a general member of becomes an irreducible non-singular surface. We also show that if and , then the last surface is a minimal surface of general type with vanishing irregularity. We also show that the rational map associated to the system is birational if and only if .

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Additional Information

**Nobuhiro Honda**

Affiliation:
Department of Mathematics, Tokyo Institute of Technology, O-okayama, Tokyo, Japan

Email:
honda@math.titech.ac.jp

DOI:
https://doi.org/10.1090/S0002-9939-09-10207-1

Received by editor(s):
June 29, 2009

Received by editor(s) in revised form:
September 7, 2009, and September 15, 2009

Published electronically:
December 8, 2009

Additional Notes:
The author was partially supported by the Grant-in-Aid for Young Scientists (B), The Ministry of Education, Culture, Sports, Science and Technology, Japan.

Communicated by:
Jon G. Wolfson

Article copyright:
© Copyright 2009
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.