Remarks on Galois rational covers

TL;DR

This paper refines the understanding of Galois rational covers for primitive Fano varieties by broadening the applicable Galois groups and relaxing conditions on the variety, specifically divisorial canonicity.

Contribution

It extends the class of Galois groups for which the theorem applies and shows divisorial canonicity alone suffices for the results.

Findings

Broadened the class of Galois groups compatible with the theorem

Relaxed conditions on the variety to divisorial canonicity

Improved the theorem on Galois rational covers for primitive Fano varieties

Abstract

In this note we improve the theorem on Galois rational covers $X\dashrightarrow V$ for primitive Fano varieties $V$, recently proven by the author, in the two directions: we extend to the maximum the class of Galois groups $G$, for which the proof works, and relax the conditions that must be satisfied by the variety $V$ -- the divisorial canonicity alone is sufficient.