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<p>In this article, we compute Seshadri constants of ample line bundles on the blowup of Hirzebruch surface <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {F}_e\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">F</mi> <mi>e</mi> </msub> </math></EquationSource> </InlineEquation> at <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(r\leqslant e+3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>r</mi> <mo>⩽</mo> <mi>e</mi> <mo>+</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation> very general points. Similarly, we compute Seshadri constants on the blowups of certain decomposable ruled surfaces over smooth curves of non-zero genus. We also prove some results related to bounded negativity of blowups of Hirzebruch surfaces and ruled surfaces.</p>

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Seshadri constants and negative curves on blowups of ruled surfaces

  • 期刊论文

  • 发表日期：

    2026年5月6日

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  • Cyril J. Jacob,
  • Bivas Khan,
  • Ronnie Sebastian

摘要

In this article, we compute Seshadri constants of ample line bundles on the blowup of Hirzebruch surface \(\mathbb {F}_e\) F e at \(r\leqslant e+3\) r ⩽ e + 3 very general points. Similarly, we compute Seshadri constants on the blowups of certain decomposable ruled surfaces over smooth curves of non-zero genus. We also prove some results related to bounded negativity of blowups of Hirzebruch surfaces and ruled surfaces.