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<p>Let <i>C</i> be a cusp in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="25_2025_2524_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="48" /> </InlineMediaObject> <EquationSource Format="TEX">\(({\mathbb {C}}^2,{\textbf{0}})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mn>2</mn> </msup> <mo>,</mo> <mn mathvariant="bold">0</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> with Puiseux pair (<i>n</i>,&#xa0;<i>m</i>). This paper is devoted to show how the semimodule of differential values of <i>C</i> determines a subset of the roots of the Bernstein-Sato polynomial of <i>C</i>. We add more precise results when the multiplicity of the cusp is <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="25_2025_2524_Article_IEq2.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\(n\le 4\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>≤</mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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From Differential Values to Roots of the Bernstein-Sato Polynomial

  • 期刊论文

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  • 发表日期：

    2025年9月25日

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  • David Senovilla-Sanz

摘要

Let C be a cusp in \(({\mathbb {C}}^2,{\textbf{0}})\) ( C 2 , 0 ) with Puiseux pair (n, m). This paper is devoted to show how the semimodule of differential values of C determines a subset of the roots of the Bernstein-Sato polynomial of C. We add more precise results when the multiplicity of the cusp is \(n\le 4\) n ≤ 4 .