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<p>The moduli space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {S}_{g, 2n}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">S</mi> <mrow> <mi>g</mi> <mo>,</mo> <mn>2</mn> <mi>n</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> parametrizes pointed curves with spin structure. We prove that <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal {S}_{2, 4}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">S</mi> <mrow> <mn>2</mn> <mo>,</mo> <mn>4</mn> </mrow> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathcal {S}_{2, 6}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">S</mi> <mrow> <mn>2</mn> <mo>,</mo> <mn>6</mn> </mrow> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\mathcal {S}_{3, 2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">S</mi> <mrow> <mn>3</mn> <mo>,</mo> <mn>2</mn> </mrow> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathcal {S}_{3, 4}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">S</mi> <mrow> <mn>3</mn> <mo>,</mo> <mn>4</mn> </mrow> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\mathcal {S}_{3, 6}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">S</mi> <mrow> <mn>3</mn> <mo>,</mo> <mn>6</mn> </mrow> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\mathcal {S}_{4, 2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">S</mi> <mrow> <mn>4</mn> <mo>,</mo> <mn>2</mn> </mrow> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\mathcal {S}_{4, 4}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">S</mi> <mrow> <mn>4</mn> <mo>,</mo> <mn>4</mn> </mrow> </msub> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\mathcal {S}_{5, 2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">S</mi> <mrow> <mn>5</mn> <mo>,</mo> <mn>2</mn> </mrow> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(\mathcal {S}_{5, 4}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">S</mi> <mrow> <mn>5</mn> <mo>,</mo> <mn>4</mn> </mrow> </msub> </math></EquationSource> </InlineEquation> are uniruled.</p>

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Uniruledness of some moduli spaces of pointed spin curves

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  • 发表日期：

    2026年3月10日

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  • Bogdan-Petru Carasca

摘要

The moduli space \(\mathcal {S}_{g, 2n}\) S g , 2 n parametrizes pointed curves with spin structure. We prove that \(\mathcal {S}_{2, 4}\) S 2 , 4 , \(\mathcal {S}_{2, 6}\) S 2 , 6 , \(\mathcal {S}_{3, 2}\) S 3 , 2 , \(\mathcal {S}_{3, 4}\) S 3 , 4 , \(\mathcal {S}_{3, 6}\) S 3 , 6 , \(\mathcal {S}_{4, 2}\) S 4 , 2 , \(\mathcal {S}_{4, 4}\) S 4 , 4 , \(\mathcal {S}_{5, 2}\) S 5 , 2 and \(\mathcal {S}_{5, 4}\) S 5 , 4 are uniruled.