Rational surfaces with

Author:
Brian Harbourne

Journal:
Proc. Amer. Math. Soc. **124** (1996), 727-733

MSC (1991):
Primary 14C20, 14J26; Secondary 13D40, 13P99

DOI:
https://doi.org/10.1090/S0002-9939-96-03226-1

MathSciNet review:
1307526

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Abstract | References | Similar Articles | Additional Information

Abstract: The main but not all of the results in this paper concern rational surfaces for which the self-intersection 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 Nebraska-Lincoln, Lincoln, Nebraska 68588-0323

Email:
bharbourne@unl.edu

DOI:
https://doi.org/10.1090/S0002-9939-96-03226-1

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