Remarks on the positivity of the cotangent bundle of an Enriques surface

Abstract

Let $S$ be a very general Enriques surface. In this paper we show that ${\Omega }_S{|}_C$ is semistable for a general curve $C\in |H|$, where $H$ is an effective line bundle on $S$. Moreover, we give explicit constructions of families of smooth irreducible curves that destabilize ${\Omega }_S$

The previous version contained an error in the proof of Theorem A. The proof has now been corrected under the assumption that (S) is a very general Enriques surface