The cones of effective cycles on projective bundles over curves

Abstract

Generalizing work done by Miyaoka and others in the case of divisors and of curves, we compute the cones of effective cycles of arbitrary dimension on a projective bundle over a complex projective curve in terms of the numerical data in an associated Harder-Narasimhan filtration. An application to cycles on projective bundles over a smooth complex projective base of arbitrary dimension is also given.

arXiv commentv2: fixed some typos, and an error in the introduction where numerical spaces were defined as subspaces in cohomology