The most symmetric smooth cubic surface
Anastasia V. Vikulova
TL;DR
This paper determines the largest automorphism group of smooth cubic surfaces over fields with characteristic not equal to 2 and proves the uniqueness of such surfaces up to isomorphism.
Contribution
It identifies the maximal automorphism group for smooth cubic surfaces over specified fields and establishes their uniqueness up to isomorphism.
Findings
Largest automorphism group characterized
Uniqueness of the surface with maximal symmetry proven
Results hold for fields with characteristic not 2
Abstract
In this paper for any field of characteristic different from 2 we find the largest automorphism group of a smooth cubic surface over this field. Moreover, we prove that for a given field a smooth cubic surface with the largest automorphism group is unique up to isomorphism.
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Taxonomy
TopicsMathematics and Applications · Computational Geometry and Mesh Generation · Geometric and Algebraic Topology