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arXiv · 1804.09469

On the Cayley-Bacharach Property

Martin Kreuzer·Le Ngoc Long·Lorenzo Robbiano
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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.

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Martin Kreuzer, Le Ngoc Long, Lorenzo Robbiano. 2018-04-25. On the Cayley-Bacharach Property. https://arxiv.org/abs/1804.09469

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