Demailly's Conjecture for general and very general points

Abstract

We prove that at least ${\left(\frac{(1+\hat{I}\mu )2m}{N-1}+1+\hat{I}\mu \right)}^N$, where $0⩽\hat{I}\mu <1$, many general points, satisfy Demailly's conjecture. Previously, it was known to be true for at least $(2m+2{)}^N$ many general points in arxiv.org/abs/2009.05022. We also study Demailly's conjecture for $m=3$ for ideal defining general and very general points.

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