Automorphisms of prime power order of weighted hypersurfaces

TL;DR

This paper investigates automorphisms of weighted hypersurfaces, providing criteria and bounds for prime order automorphisms, and introduces a weighted Klein hypersurface that maximizes prime automorphism order.

Contribution

It extends classical automorphism results to weighted hypersurfaces, establishing explicit bounds and identifying a maximal prime order automorphism example.

Findings

Derived effective criteria for prime power automorphism orders.

Established explicit bounds on possible prime automorphism orders.

Identified a weighted Klein hypersurface realizing maximal prime automorphism order.

Abstract

We study automorphisms of quasi-smooth hypersurfaces in weighted projective spaces, extending classical results for smooth hypersurfaces in projective space to the weighted setting. We establish effective criteria for when a power of a prime number can occur as the order of an automorphism, and we derive explicit bounds on the possible prime orders. A key role is played by a weighted analogue of the classical Klein hypersurface, which we show realizes the maximal prime order of an automorphism under suitable arithmetic conditions. Our results generalize earlier work by Gonz\'alez-Aguilera and Liendo.