Abstract: Let X be a projective scheme over an algebraically closed field. Given a vector bundle E on X, we can consider various notions of positivity for E, such as ample, nef, and big. As a particular example, consider a smooth projective variety X and its cotangent bundle X. When X is ample, X has some very nice properties. For example, all subvarieties of X are of general type and X is algebraically hyperbolic; so, in particular, X does not contain rational or elliptic curves and there do not exist nonconstant maps f : A → X where A is an abelian variety and X is Kobayashi hyperbolic [3]. Requiring that the cotangent bundle be ample is certainly a very strong property, and for a long time there were few examples of such varieties even though they were expected to be reasonably abundant. One such example was constructed by Michael Schneider.