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

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.

12 pages, 1 figure. Minor modifications, citations added, acknowledged a result which was known in the literature

References in corpus (2)

• Bound on the multiplicity of almost complete intersections
• Cayley-Bacharach theorems with excess vanishing