Cohen-Macaulay modules on quadrics
Cohen-Macaulay modules on quadrics
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二次曲面上的 Cohen-Macaulay 模
DOI：
10.1007/bfb0078838
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发表时间：
1987
期刊：
影响因子：
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通讯作者：
J. Herzog
中科院分区：
文献类型：
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作者：
R. Buchweitz;D. Eisenbud;J. Herzog
本文研究了R=k[x1，…，xr]/Q，当Q是定义正则射影超曲面的二次型，且k是任意域（当k是特征为λ 2的代数闭域时的情况是Knorrer [1986]发展的理论的特例）。对任意非零二次型Q，正则的或非正则的，分次极大Cohen-Macaulay R-模定义了Q的偶Clifford代数上的模，并且证明了该代数是半单的当且仅当Q是正则的（这对于char k <$2是经典的）.由于这一点和其他信息的Clifford代数，我们给一个详细的帐户的科恩-麦考利模时，Q是正规的，确定的数量不可分解（2或3，计数R）的行列，以及它们之间的关系的对偶性和syzygy。
This paper analyzes the graded maximal Cohen-Macaulay modules over rings of the form R=k[x1,...,xr]/Q, when Q is a quadratic form defining a regular projective hypersurface, and k is an arbitrary field (the case when k is algebraically closed of characteristic ≠2 is a special case of the theory developed by Knorrer [1986]). For any nonzero quadratic form Q, regular or not, the graded maximal Cohen-Macaulay R-modules define modules over the even Clifford algebra of Q, and we show that this algebra is semi-simple iff Q is regular (this is classical for char k ≠2). As a result of this and other information about the Clifford algebra, we give a detailed account of the Cohen-Macaulay modules when Q is regular, identifying the number of indecomposables (2 or 3, counting R) their ranks, and the relations of duality and syzygy among them.