Projective Automorphism Groups of Nonsingular Quartic Surfaces

TL;DR

This paper classifies nonsingular quartic surfaces in three-dimensional projective space that are invariant under cyclic groups of prime order p, and determines their automorphism groups in certain cases.

Contribution

It provides a complete classification of Z_p-invariant nonsingular quartic surfaces and identifies their automorphism groups for specific cases.

Findings

Classified all Z_p-invariant nonsingular quartic surfaces for p >= 5.

Determined full automorphism groups in some cases.

Enhanced understanding of symmetry groups of quartic surfaces.

Abstract

For every p >= 5, we determine all Z_p-invariant nonsingular quartic surfaces in the three dimensional projective space over an algebraically closed field of characteristic zero. In some cases, we also determine their full projective automorphism groups.