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<p>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 <i>X</i>, we consider the subgroup <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\textrm{SAut}(X)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>SAut</mtext> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> 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 <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\textrm{SAut}(X)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>SAut</mtext> <mo stretchy="false">(</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> 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.</p>

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On Flexibility of Trinomial Varieties

  • 期刊论文

  • 发表日期：

    2026年2月26日

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  • Mikhail Ignatev,
  • Timofey Vilkin

摘要

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 \(\textrm{SAut}(X)\) 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 \(\textrm{SAut}(X)\) 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.