Newton-Okounkov bodies on projective bundles over curves

Abstract

In this article, we study Newton-Okounkov bodies on projective vector bundles over curves. Inspired by Wolfe's estimates used to compute the volume function on these varieties, we compute all Newton-Okounkov bodies with respect to linear flags. Moreover, we characterize semi-stable vector bundles over curves via Newton-Okounkov bodies.

arXiv comment28 pages. Final version: to appear in Mathematische Zeitschrift