Automorphisms of prime power order of weighted hypersurfaces

Alvaro Liendo; Ana Julisa Palomino

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arXiv · 2507.13538

Automorphisms of prime power order of weighted hypersurfaces

Alvaro Liendo·Ana Julisa Palomino

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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.

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Alvaro Liendo, Ana Julisa Palomino. 2025-07-17. Automorphisms of prime power order of weighted hypersurfaces. https://arxiv.org/abs/2507.13538

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