The genus-minimizing property of algebraic curves
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- by P. B. Kronheimer PDF
- Bull. Amer. Math. Soc. 29 (1993), 63-69 Request permission
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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- 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