On Chern ratios for surfaces with ample cotangent bundle

Abstract

In this paper we study the problem of density in (1, 3) for the Chern ratio of surfaces with ample cotangent bundle. In particular we prove density in (1, 2) by constructing a family of complete intersection surfaces in a product of varieties with big cotangent bundle. We also analyse the case of complete intersections in a product of curves of genus at least 2.