Convex Fujita numbers are not determined by the fundamental group

Abstract

We study effective global generation of adjoint line bundles on smooth projective varieties. To measure the effectivity we introduce the concept of the convex Fujita number of a smooth projective variety and compute its value for a class of varieties with prescribed dimension $d\ge 2$ and an arbitrary projective group as fundamental group.

Title changed. Accepted version, to appear in Adv. Geom