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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Distinguishing embedded curves
in rational complex surfaces


Author: Terry Fuller
Journal: Proc. Amer. Math. Soc. 126 (1998), 305-310
MSC (1991): Primary 57R40; Secondary 14J26
MathSciNet review: 1416086
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Abstract: We construct many pairs of smoothly embedded complex curves with the same genus and self-intersection number in the rational complex surfaces $\mathbb{C} P^{2}\# n\overline{\mathbb{C} P}^{2}$ with the property that no self-diffeomorphism of $\mathbb{C} P^{2} \# n \overline{\mathbb{C} P}^{2}$ sends one to the other. In particular, as a special case we answer a question originally posed by R. Gompf (1995) concerning genus two curves of self-intersection number 0 in $\mathbb{C} P^{2} \# 13\overline{\mathbb{C} P}^{2} $.


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Additional Information

Terry Fuller
Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
Address at time of publication: Department of Mathematics, University of California, Irvine, California 92717
Email: tfuller@math.uci.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04001-5
PII: S 0002-9939(98)04001-5
Keywords: Rational complex surface, embedded surface, branched cover, normal sum
Received by editor(s): April 22, 1996
Received by editor(s) in revised form: July 9, 1996
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 1998 American Mathematical Society