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Exceptional curves on smooth rational surfaces with  not nef and of self-intersection zero
Author(s):
Mustapha
Lahyane
Journal:
Proc. Amer. Math. Soc.
133
(2005),
1593-1599.
MSC (2000):
Primary 14J26;
Secondary 14F05
Posted:
December 31, 2004
MathSciNet review:
2120267
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Abstract:
A  -curve is a smooth rational curve of self-intersection  , where  is a positive integer. In 1998 Hirschowitz asked whether a smooth rational surface  defined over the field of complex numbers, having an anti-canonical divisor not nef and of self-intersection zero, has  -curves. In this paper we prove that for such a surface  , the set of  -curves on  is finite but non-empty, and that  may have no  -curves. Related facts are also considered.
References:
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Additional Information:
Mustapha
Lahyane
Affiliation:
Abdus Salam International Centre for Theoretical Physics, 34100 Trieste, Italy
Address at time of publication:
Departamento de Álgebra, Geometría y Topología, Facultad de Ciencias, Vallodolid University, 47005 Valladolid, Spain
Email:
lahyane@agt.uva.es
DOI:
10.1090/S0002-9939-04-07693-2
PII:
S 0002-9939(04)07693-2
Keywords:
Anticanonical rational surfaces,
minimal models of smooth rational surfaces,
Hodge Index Theorem,
points in general position,
N\'eron-Severi group,
blowing-up
Received by editor(s):
August 27, 2001
Received by editor(s) in revised form:
February 23, 2004
Posted:
December 31, 2004
Additional Notes:
This work was partially supported by a postdoctoral fellowship at the International Centre for Theoretical Physics (Trieste, Italy) and by a Marie Curie grant number HPMD-GH-01-00097-01 at the Department of ``Álgebra, Geometría y Topología'' of the Valladolid University (Valladolid, Spain).
Communicated by:
Michael Stillman
Copyright of article:
Copyright
2004,
American Mathematical Society
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