SYZYGIES OF CRITICAL RANK
SYZYGIES OF CRITICAL RANK
复制标题
DOI：
10.1093/qmath/35.4.393
复制
发表时间：
1984-12
影响因子：
0.7
通讯作者：
E. Evans;Phillip Criffith
中科院分区：
文献类型：
--
作者：
E. Evans;Phillip Criffith
设(R，m，I)是d的正则局部环，M是有限生成的自反模。在[1]中，Auslander和Bridger产生一个有限生成的自由模F和滤子M(BF=Mi 2···2Mj 2Md+L=0)使得Mi/Mt+L在上同调Ext‘(M，/Mi+L，本文讨论了当R的穿孔谱上有向量丛的情况下，Horrocks[8]的对偶滤波是什么.我们在第一节中给出了滤子的构造.在第二节中，我们证明了如果M是一个秩为Fc的函数并如果R包含一个域，则这种滤子具有特殊的形式.特别地，我们得出结论：如果M是Fc阶的fc合子，则M可以表示为B/S，其中B是Extk“1(M*，R)的fc合子，S是(fc+2)nd合子。我们在第二节讨论了B和S的构造及其唯一性。最后在第三节讨论了向量丛在图的穿孔谱上的特殊情况
LET (R, m, I) be a regular local ring of dimension d. Let M be a finitely generated reflexive module. In [1] Auslander and Bridger produce a finitely generated free module F and filtration M (BF= Mi 2••• 2 Mj 2 Md+ l= 0 such that Mi/Mt+ l are" spherical" in the sense that the cohomology Ext'(M,/Mi+ l, R) is nonzero only if/is equal to 0 or i. In this article we discuss what is in effect the dual filtration of Horrocks [8] for the case of vector bundles on the punctured spectrum of R. We give the construction of the filtration in Section 1. In Section 2 we show that if M is a fcth syzygy of rank fc and if R contains a field, then the filtration takes a special form. In particular we conclude that if M is a fcth syzygy of rank fc then M can be presented as B/S, where B is a fcth syzygy of Extk" 1 (M*, R) and S is (fc+ 2) nd syzygy. We discuss the construction of B and S as well as their uniqueness in Section 2. Finally in Section 3 we discuss the particular case of vector bundles on the punctured spectrum of