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arXiv · 1604.02217

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

Louiza Fouli·Paolo Mantero·Yu Xie
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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 $R=k[x_0, \ldots, x_N]$, Chudnovsky's conjecture holds for large enough symbolic powers of $I$.

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Louiza Fouli, Paolo Mantero, Yu Xie. 2016-04-08. Chudnovsky's Conjecture for very general points in $\mathbb{P}_k^{N}$. https://arxiv.org/abs/1604.02217

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