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

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

2011-04-12

arxiv.org/abs/1104.2263v1

Mathematics

Algebraic Geometry

11 pages

Scientific paper

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.

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