The genus-minimizing property of algebraic curves

Peter B. Kronheimer

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arXiv · math/9307230

The genus-minimizing property of algebraic curves

Peter B. Kronheimer

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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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Peter B. Kronheimer. 1993-07-01. The genus-minimizing property of algebraic curves. https://arxiv.org/abs/math/9307230

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