We investigate Demailly's Conjecture for a general set of sufficiently many points. Demailly's Conjecture generalizes Chudnovsky's Conjecture in providing a lower bound for the Waldschmidt constant of a set of points in projective space. We also study a containment between symbolic and ordinary powers conjectured by Harbourne and Huneke that in particular implies Demailly's bound, and prove that a general version of this containment holds for generic determinantal ideals and defining ideals of star configurations.

中文翻译：

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Demailly 猜想和遏制问题

我们针对一组足够多的点研究 Demailly 猜想。Demailly's Conjecture 概括了 Chudnovsky's Conjecture，为投影空间中的一组点的 Waldschmidt 常数提供了下界。我们还研究了 Harbourne 和 Huneke 推测的象征性权力和普通权力之间的包含，特别暗示了 Demailly 的界限，并证明了这种包含的一般版本适用于一般的决定性理想和定义恒星配置的理想。