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<p>Let <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(n=\frac{r(r+1)}{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>=</mo> <mfrac> <mrow> <mi>r</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mn>2</mn> </mfrac> </mrow> </math></EquationSource> </InlineEquation> or <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(n=2r(r+1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>=</mo> <mn>2</mn> <mi>r</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo>+</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. We prove that the property of being extremal is preserved under residuality for divisors in the Hilbert scheme of <i>n</i> points in the plane.</p>

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Extremal divisors in the Hilbert scheme of points on \(\mathbb {P}^{2}\) are preserved under residuality

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  • 发表日期：

    2026年6月29日

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  • Montserrat Vite

摘要

Let \(n=\frac{r(r+1)}{2}\) n = r ( r + 1 ) 2 or \(n=2r(r+1)\) n = 2 r ( r + 1 ) . We prove that the property of being extremal is preserved under residuality for divisors in the Hilbert scheme of n points in the plane.