Irreducibility of the -classes on smooth rational surfaces
Proc. Amer. Math. Soc. 133 (2005), 2219-2224
Primary 14J26; Secondary 14F05
March 14, 2005
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Abstract: We give a characterization for a -divisor on a smooth rational surface to be irreducible under the assumption that an anticanonical divisor of is nef. Here is nef means for every effective divisor on , and a -divisor is a divisor such that the two numerical conditions hold.
As an application we give explicit examples of blowing up the projective plane at nine points infinitely near such that the obtained surface has an infinite number of -curves. A -curve is a smooth rational curve of self-intersection .
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Abdus Salam International Centre for Theoretical Physics, 34100 Trieste, Italy
Address at time of publication:
Departamento de Àlgebra, Geometrìa y Topologìa, Facultad de Ciencias, 47005 Valladolid, Spain
Smooth rational surfaces,
Hodge Index Theorem,
points in general position,
Received by editor(s):
June 28, 2001
Received by editor(s) in revised form:
October 15, 2003
March 14, 2005
The author was partially supported by a postdoctoral fellowship at the International Centre for Theoretical Physics (Trieste, Italy) and a Marie Curie grant number HPMD-GH-01-00097-01 at the department of “Álgebra, Geometría y Topología” of Valladolid University (Valladolid, Spain).
This research is dedicated to my mother, Hnia Hamami
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American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.