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<p>In this work, we describe a prenormal form for the generators of the semigroup of a toric variety <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(X \subset \mathbb {C}^p\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>X</mi> <mo>⊂</mo> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mi>p</mi> </msup> </mrow> </math></EquationSource> </InlineEquation> with isolated singularity at the origin and smooth normalization. A complete description of the semigroup is given when <i>X</i> is a variety of dimension <i>n</i> in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {C}^{2n}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </msup> </math></EquationSource> </InlineEquation>. Moreover, for toric surfaces in <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb {C}^4\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mn>4</mn> </msup> </math></EquationSource> </InlineEquation>, we provide a set of generators of the ideal <i>I</i> defining <i>X</i>.</p>

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Toric Varieties with Isolated Singularity and Smooth Normalization

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月29日

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  • Thaís Maria Dalbelo,
  • Maria Elenice Rodrigues Hernandes,
  • Maria Aparecida Soares Ruas

摘要

In this work, we describe a prenormal form for the generators of the semigroup of a toric variety \(X \subset \mathbb {C}^p\) X ⊂ C p with isolated singularity at the origin and smooth normalization. A complete description of the semigroup is given when X is a variety of dimension n in \(\mathbb {C}^{2n}\) C 2 n . Moreover, for toric surfaces in \(\mathbb {C}^4\) C 4 , we provide a set of generators of the ideal I defining X.