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On flexibility of trinomial varieties

2025/06/25 by Mikhail Ignatev, Ignatev, Mikhail, Timofey Vilkin +1
Computer Science · Engineering · #13N15 #14J50 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Polynomial and algebraic computation #primary 14R20 #secondary 13A50

paper · pdf · doi:10.48550/arxiv.2506.20524

openalex publication_date 2025/06/25 · openalex created_date 2025/10/09 · openalex updated_date 2026/07/28

Abstract

Trinomial varieties are affine varieties given by a system of equations consisting of polynomials with three terms. Such varieties are total coordinate spaces of normal varieties with torus action of complexity one. For an affine variety X we consider the subgroup SAut(X) of the automorphism group generated by all algebraic subgroups isomorphic to the additive group of the ground field. By definition, an affine variety is flexible if SAut(X) acts transitively on its regular locus. Gaifullin proved a sufficient condition for a trinomial hypersurface to be flexible. We give a generalization of his results, proving a sufficient condition to be flexible for an arbitrary trinomial variety.

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