Gromov's ellipticity of principal $G_m$-bundles

TL;DR

This paper proves that all nontrivial principal G_m-bundles over complete uniformly rational varieties are algebraically elliptic, extending Gromov's notion of ellipticity to this class of bundles.

Contribution

It establishes the algebraic ellipticity of principal G_m-bundles over a broad class of varieties, generalizing previous results in the field.

Findings

Nontrivial principal G_m-bundles are algebraically elliptic.

The result applies to complete uniformly rational varieties.

Extension of Gromov's ellipticity concept to new geometric structures.

Abstract

We prove that every nontrivial principal $G_m$-bundle over a complete uniformly rational variety is algebraically elliptic in the sense of Gromov.