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<p>The aim of this paper is to provide an explicit basis of the miniversal deformation of a monomial curve defined by a free semigroup—these curves make up a notable family <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathscr {C}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">C</mi> </math></EquationSource> </InlineEquation> of complete intersection monomial curves. First, we dispense a general decomposition result of a basis <i>B</i> of the miniversal deformation of any complete intersection monomial curve. As a consequence, we explicitly calculate <i>B</i> in the particular case of a monomial curve defined from a free semigroup. This direct computation yields some estimates for the dimension of the moduli space of the family <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathscr {C}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">C</mi> </math></EquationSource> </InlineEquation>.</p>

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The miniversal deformation of certain complete intersection monomial curves

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月29日

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  • Patricio Almirón,
  • Julio José Moyano-Fernández

摘要

The aim of this paper is to provide an explicit basis of the miniversal deformation of a monomial curve defined by a free semigroup—these curves make up a notable family \(\mathscr {C}\) C of complete intersection monomial curves. First, we dispense a general decomposition result of a basis B of the miniversal deformation of any complete intersection monomial curve. As a consequence, we explicitly calculate B in the particular case of a monomial curve defined from a free semigroup. This direct computation yields some estimates for the dimension of the moduli space of the family \(\mathscr {C}\) C .