On a plane section of an integral curve in positive characteristic

Abstract

If $C\subset P_k^3$ is an integral curve and $k$ an algebraically closed field of characteristic 0, it is known that the points of the general plane section $C\cap H$ of $C$ are in uniform position. From this it follows easily that the general minimal curve containing $C\cap H$ is irreducible. If $chark=p>0$, the points of $C\cap H$ may not be in uniform position. However, we prove that the general minimal curve containing $C\cap H$ is still irreducible.