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<p>We prove Demailly’s Conjecture concerning the lower bound for the Waldschmidt constant in terms of the initial degree of the second symbolic powers for any set of very general points in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathbb {P}}^N\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">P</mi> </mrow> <mi>N</mi> </msup> </math></EquationSource> </InlineEquation>. We also discuss the Harbourne-Huneke Containment and the aforementioned Demailly’s Conjecture for general points and show the results for sufficiently many general points and general points in projective spaces with low dimensions.</p>

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Lower bounds for Waldschmidt constants and Demailly’s conjecture for general and very general points

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  • 发表日期：

    2025年5月9日

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  • Sankhaneel Bisui,
  • Thái Thành Nguyễn

摘要

We prove Demailly’s Conjecture concerning the lower bound for the Waldschmidt constant in terms of the initial degree of the second symbolic powers for any set of very general points in \({\mathbb {P}}^N\) P N . We also discuss the Harbourne-Huneke Containment and the aforementioned Demailly’s Conjecture for general points and show the results for sufficiently many general points and general points in projective spaces with low dimensions.