Convex Fujita numbers are not determined by the fundamental group

TL;DR

This paper introduces the convex Fujita number to measure the effectiveness of global generation of adjoint line bundles on smooth projective varieties and computes its value for varieties with specified dimension and fundamental group.

Contribution

It defines the convex Fujita number and calculates its value for varieties with given dimension and arbitrary fundamental group.

Findings

Convex Fujita numbers are computed for certain classes of varieties.

The study links the convex Fujita number to the fundamental group.

Results provide new insights into the effectivity of line bundles on algebraic varieties.

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 $d \geq 2$ and an arbitrary projective group as fundamental group.