Automorphisms of Galois Coverings of Generic $m$-Canonical Projections

TL;DR

This paper investigates the automorphism groups of Galois coverings arising from generic pluri-canonical projections, revealing new series of symmetric group actions on curves and surfaces that are not deformable to smaller automorphism groups.

Contribution

It introduces new series of symmetric group actions on algebraic varieties via Galois coverings, expanding understanding of automorphism groups in complex geometry.

Findings

Identifies specific symmetric group actions on curves and surfaces in dimensions one and two.

Shows these actions are not deformable to smaller automorphism groups.

Provides new examples of G-varieties with distinct automorphism and deformation properties.

Abstract

The automorphism group of the Galois covering induced by a pluri-canonical generic covering of a projective space is investigated. It is shown that by means of such coverings one obtains, in dimensions one and two, serieses of specific actions of the symmetric groups $S_d$ on curves and surfaces not deformable to an action of $S_d$ which is not the full automorphism group. As an application, new DIF $\ne$ DEF examples for $G$-varieties in complex and real geometry are given.