论文标题
带有贝蒂数字的完美模块$（2,6,5,1）$
Perfect modules with Betti numbers $(2,6,5,1)$
论文作者
论文摘要
在2018年，Celikbas，Laxmi，Kraśkiewicz和Weyman在Cohen-Macaulay二型二型二号发电机中展示了一个有趣的组成的完美理想。 Brown在1987年发现了所有以前已知的Condimension 3的完美理想，以及五个发电机的Cohen-Macaulay。我们证明，棕色的所有理想都是从Celikbas，Laxmi，Kraśkiewicz和Weyman的理想中获得的。我们还证明，当使用电源系列变量在一个字段上建立的理想家族时，在Lichtebaum和Schlessinger的意义上定义了刚性代数。
In 2018 Celikbas, Laxmi, Kraśkiewicz, and Weyman exhibited an interesting family of perfect ideals of codimension three, with five generators, of Cohen-Macaulay type two with trivial multiplication on the Tor algebra. All previously known perfect ideals of codimension three, with five generators, of Cohen-Macaulay type two had been found by Brown in 1987. Brown's ideals all have non-trivial multiplication on the Tor algebra. We prove that all of the ideals of Brown are obtained from the ideals of Celikbas, Laxmi, Kraśkiewicz, and Weyman by (non-homogeneous) specialization. We also prove that both families of ideals, when built using power series variables over a field, define rigid algebras in the sense of Lichtenbaum and Schlessinger.
