A Cayley-Bacharach theorem for points in $\mathbb{P}^n$

TL;DR

This paper extends the Cayley-Bacharach theorem to points in projective space , establishing new bounds on the Hilbert function of almost complete intersections to facilitate the proof.

Contribution

It introduces a Cayley-Bacharach-type theorem for points in  and provides novel bounds on the Hilbert function of almost complete intersections.

Findings

Proves a Cayley-Bacharach-type theorem in .

Establishes new bounds on the Hilbert function growth.

Enables applications to algebraic geometry problems.

Abstract

We prove a Cayley-Bacharach-type theorem for points in projective space $\mathbb{P}^n$ that lie on a complete intersection of $n$ hypersurfaces. This is made possible by new bounds on the growth of the Hilbert function of almost complete intersections.