Automorphisms of rigid hypersurfaces with separable variables

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...

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Bibliographic Details
Main Author Trushin, Anton
Format Journal Article
LanguageEnglish
Published 12.07.2024
Subjects
Mathematics - Algebraic Geometry
Mathematics - Rings and Algebras
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Summary: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.
DOI:10.48550/arxiv.2407.09235