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Maximal Cohen-Macaulay modules over \(Y^3_1+\cdots+Y^3_n\) with few generators. (English) Zbl 1026.13005

Summary: Let \(R_n=K[Y_1,\dots, Y_n]/(f_n)\), \(f_n=Y_1^3+\cdots+Y_n^3\), where \(K\) is an algebraically closed field with \(\operatorname {char}K\neq 3\). We give a bijection between the isomorphism classes of two-generated, maximal Cohen-Macaulay, non-free graded \(R_3\)-modules, and the points of the curves \(V(f_3)\subset \mathbb{P}^2_K\). In a different form this bijection seems to appear also in a paper by C. P. Kahn [Math. Ann. 285, No. 1, 141-160 (1989; Zbl 0662.14022)]. For \(n>3\) we study the minimal number of generators of a maximal Cohen-Macaulay, non-free graded \(R_n\)-module.

MSC:

13C14 Cohen-Macaulay modules

Citations:

Zbl 0662.14022
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