Chudnovsky's Conjecture for very general points in ${\mathbb{P}}_k^N$

Abstract

We prove a long-standing conjecture of Chudnovsky for very general and generic points in ${\mathbb{P}}_k^N$, where $k$ is an algebraically closed field of characteristic zero, and for any finite set of points lying on a quadric, without any assumptions on $k$. We also prove that for any homogeneous ideal $I$ in the homogeneous coordinate ring $R=k[x_0,\dots ,x_N]$, Chudnovsky's conjecture holds for large enough symbolic powers of $I$.

Revised version to appear in Journal of Algebra

References in corpus (2)

• Are symbolic powers highly evolved?
• A containment result in ${\mathbb{P}}^n$ and the Chudnovsky conjecture

Cited by in corpus (1)

• On a conjecture of Demailly and new bounds on Waldschmidt constants in ${\mathbb{P}}^N$