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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

The genus-minimizing property of algebraic curves


Author: P. B. Kronheimer
Journal: Bull. Amer. Math. Soc. 29 (1993), 63-69
MSC (2000): Primary 57R57; Secondary 14J99, 57R40, 58D27
MathSciNet review: 1193539
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Abstract: A viable and still unproved conjecture states that, if X is a smooth algebraic surface and C is a smooth algebraic curve in X, then C realizes the smallest possible genus amongst all smoothly embedded 2-manifolds in its homology class. A proof is announced here for this conjecture, for a large class of surfaces X, under the assumption that the normal bundle of C has positive degree.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0273-0979-1993-00399-9
PII: S 0273-0979(1993)00399-9
Article copyright: © Copyright 1993 American Mathematical Society