The genus-minimizing property of algebraic curves

Peter B. Kronheimer

The genus-minimizing property of algebraic curves

Geometric Topology 2016-09-06 v1 Differential Geometry

Authors: Peter B. Kronheimer

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.

Keywords

algebraic curve smooth algebraic surface genus minimization homology class normal bundle

Cite

@article{arxiv.math/9307230,
  title  = {The genus-minimizing property of algebraic curves},
  author = {Peter B. Kronheimer},
  journal= {arXiv preprint arXiv:math/9307230},
  year   = {2016}
}

Comments

7 pages

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