On the Cayley-Bacharach Property
Commutative Algebra
2018-10-09 v2
Abstract
The Cayley-Bacharach property, which has been classically stated as a property of a finite set of points in an affine or projective space, is extended to arbitrary 0-dimensional affine algebras over arbitrary base fields. We present characterizations and explicit algorithms for checking the Cayley-Bacharach property directly, via the canonical module, and in combination with the property of being a locally Gorenstein ring. Moreover, we characterize strict Gorenstein rings by the Cayley-Bacharach property and the symmetry of their affine Hilbert function, as well as by the strict Cayley-Bacharach property and the last difference of their affine Hilbert function.
Cite
@article{arxiv.1804.09469,
title = {On the Cayley-Bacharach Property},
author = {Martin Kreuzer and Le Ngoc Long and Lorenzo Robbiano},
journal= {arXiv preprint arXiv:1804.09469},
year = {2018}
}
Comments
27 pages; multiple minor corrections; to appear in Comm. Alg