Hypersurfaces with large automorphism groups

TL;DR

This paper establishes precise upper limits on the size of automorphism groups for hypersurfaces in complex projective spaces across all dimensions and degrees, identifying unique hypersurfaces that attain these bounds and providing explicit automorphism generators.

Contribution

It provides sharp upper bounds on automorphism group orders for hypersurfaces and characterizes the unique hypersurfaces achieving these bounds, including explicit automorphism generators.

Findings

Sharp upper bounds for automorphism groups in all dimensions and degrees

Uniqueness of hypersurfaces attaining the bounds up to isomorphism

Explicit generators for the automorphism groups

Abstract

We find sharp upper bounds on the order of the automorphism group of a hypersurface in complex projective space in every dimension and degree. In each case, we prove that the hypersurface realizing the upper bound is unique up to isomorphism and provide explicit generators for the automorphism group.