关于Cayley-Bacharach性质
On the Cayley-Bacharach Property
摘要：
Cayley-Bacharach性质是仿射空间或射影空间中有限点集的一个性质，它被推广到任意基域上的任意0维仿射代数.我们提出的特征和明确的算法检查Cayley-Bacharach属性直接，通过典型的模块，并结合本地Gorenstein环的属性。此外，我们还利用Cayley-Bacharach性质及其仿射Hilbert函数的对称性，以及严格Cayley-Bacharach性质及其仿射Hilbert函数的最后一个差刻画了严格Gorenstein环.
英文摘要：
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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