Demailly's Conjecture for general and very general points

TL;DR

This paper proves a new lower bound on the number of general points satisfying Demailly's conjecture, extending previous results and analyzing specific cases for ideal defining general and very general points.

Contribution

It establishes a generalized lower bound for the number of points satisfying Demailly's conjecture and investigates the case when m=3 for certain ideals.

Findings

New lower bound for general points satisfying Demailly's conjecture

Extension of previous results from (2m+2)^N to a more general bound

Analysis of the case m=3 for ideal defining points

Abstract

We prove that at least $\left( \dfrac{(1+\epsilon)2m}{N-1}+1+\epsilon \right)^N$, where $0\leqslant \epsilon <1$, 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.