%0 Journal Article
%T The genus-minimizing property of algebraic curves
%A Peter B. Kronheimer
%J Mathematics
%D 1993
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/9307230v1