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<p>Following the work already done by E. Looijenga and others, we provide an analysis of the deformation types of Looijenga (or anticanonical) pairs <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10711_2024_976_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="47" /> </InlineMediaObject> <EquationSource Format="TEX">\((Y,D)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>Y</mi> <mo>,</mo> <mi>D</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, where the anticanonical divisor <i>D</i> is made of <i>n</i> irreducible components and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10711_2024_976_Article_IEq2.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="73" /> </InlineMediaObject> <EquationSource Format="TEX">\(6\le n \le 9\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>6</mn> <mo>≤</mo> <mi>n</mi> <mo>≤</mo> <mn>9</mn> </mrow> </math></EquationSource> </InlineEquation>. In doing so we also give a description of their toric models.</p>

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Deformation types of Looijenga pairs of small length

  • 期刊论文

  • 发表日期：

    2025年1月27日

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  • Angelica Simonetti

摘要

Following the work already done by E. Looijenga and others, we provide an analysis of the deformation types of Looijenga (or anticanonical) pairs \((Y,D)\) ( Y , D ) , where the anticanonical divisor D is made of n irreducible components and \(6\le n \le 9\) 6 ≤ n ≤ 9 . In doing so we also give a description of their toric models.