Automorphisms of rigid hypersurfaces with separable variables

TL;DR

This paper characterizes the automorphism groups of rigid hypersurfaces with separable variables, showing they are finite extensions of their maximal tori, thus advancing understanding of their symmetry structures.

Contribution

It provides a detailed description of the automorphism group structure for rigid hypersurfaces with separable variables, highlighting their finite extension of maximal tori.

Findings

Automorphism group is a finite extension of the maximal torus.

Rigid hypersurfaces with separable variables have constrained symmetry groups.

The structure of automorphisms is explicitly characterized.

Abstract

Consider a polynomial F such that each variable appears in exactly one monomial. The hypersurface defined by the polynomial F is called a hypersurface with separable variables. A variety is called rigid if there are no nontrivial actions of the additive group of the ground field on it. If a variety is rigid, then it is known that in the automorphism group there exists a unique maximal torus. We describe the automorphism group of a rigid hypersurface with separable variables, in particular we show that it is a finite extension of the maximal torus.