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<p>Let <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(X_r\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>X</mi> <mi>r</mi> </msub> </math></EquationSource> </InlineEquation> denote the blow-up of the hyperelliptic surface <i>X</i> at <i>r</i> very general points. In this paper, we first provide a criterion for the ampleness of a line bundle on <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(X_r\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>X</mi> <mi>r</mi> </msub> </math></EquationSource> </InlineEquation> and compare it with existing results. We then study the multi-point Seshadri constants of ample line bundles on hyperelliptic surfaces <i>X</i>. Next, we compute single-point Seshadri constants on <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(X_r\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>X</mi> <mi>r</mi> </msub> </math></EquationSource> </InlineEquation> for specific ample line bundles on odd types. Furthermore, we show that the global Seshadri constants for certain ample line bundles on blow-up of hyperelliptic surfaces are rational.</p>

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Positivity on Blow-up of hyperelliptic surfaces

  • 期刊论文

  • 发表日期：

    2026年6月17日

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  • Praveen Kumar Roy

摘要

Let \(X_r\) X r denote the blow-up of the hyperelliptic surface X at r very general points. In this paper, we first provide a criterion for the ampleness of a line bundle on \(X_r\) X r and compare it with existing results. We then study the multi-point Seshadri constants of ample line bundles on hyperelliptic surfaces X. Next, we compute single-point Seshadri constants on \(X_r\) X r for specific ample line bundles on odd types. Furthermore, we show that the global Seshadri constants for certain ample line bundles on blow-up of hyperelliptic surfaces are rational.