The Picard Group of Simply Connected Regular Varieties and Stratified Line Bundles

TL;DR

This paper proves the finite generation of the Picard group for regular simply connected varieties over algebraically closed fields, and shows the absence of nontrivial stratified line bundles in positive characteristic, with a complex analog.

Contribution

It establishes the finite generation of the Picard group without relying on resolution of singularities and characterizes stratified line bundles in positive characteristic.

Findings

Picard group is finitely generated for regular simply connected varieties

No nontrivial stratified line bundles exist in positive characteristic

Provides a complex analog of the main results

Abstract

We prove that the Picard group of a regular simply connected variety over an algebraically closed field of arbitrary characteristic is finitely generated. The main difficulty to overcome is the unavailability of resolution of singularities. From this we deduce that in positive characteristic there exist no nontrivial stratified line bundles on such a variety, and we present a complex analog.