Rational surfaces with
Author:
Brian Harbourne
Journal:
Proc. Amer. Math. Soc. 124 (1996), 727733
MSC (1991):
Primary 14C20, 14J26; Secondary 13D40, 13P99
MathSciNet review:
1307526
Fulltext PDF Free Access
Abstract 
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Abstract: The main but not all of the results in this paper concern rational surfaces for which the selfintersection of the anticanonical class is positive. In particular, it is shown that no superabundant numerically effective divisor classes occur on any smooth rational projective surface with . As an application, it follows that any 8 or fewer (possibly infinitely near) points in the projective plane are in good position. This is not true for 9 points, and a characterization of the good position locus in this case is also given. Moreover, these results are put into the context of conjectures for generic blowings up of . All results are proven over an algebraically closed field of arbitrary characteristic.
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Additional Information
Brian Harbourne
Affiliation:
Department of Mathematics and Statistics University of NebraskaLincoln, Lincoln, Nebraska 685880323
Email:
bharbourne@unl.edu
DOI:
http://dx.doi.org/10.1090/S0002993996032261
PII:
S 00029939(96)032261
Keywords:
Anticanonical,
rational,
surface,
good position
Received by editor(s):
September 26, 1994
Additional Notes:
This work was supported both by the National Science Foundation and by a Spring 1994 University of Nebraska Faculty Development Leave. I would like to thank Rick Miranda and Bruce Crauder for organizing the May 1994 Mtn. West Conference, where some of the results here were presented.
Communicated by:
Eric Friedlander
Article copyright:
© Copyright 1996
American Mathematical Society
