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

DOI:
https://doi.org/10.1090/S0273-0979-1993-00399-9

MathSciNet review:
1193539

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0273-0979-1993-00399-9

Article copyright:
© Copyright 1993
American Mathematical Society