Goto, Shiro; Ozeki, Kazuho; Takahashi, Ryo; Watanabe, Kei-Ichi; Yoshida, Ken-Ichi Ulrich ideals and modules over two-dimensional rational singularities. (English) Zbl 1360.13028 Nagoya Math. J. 221, 69-110 (2016). In [“Ulrich ideals and modules,” to appear in Math. Proc. Cambridge Philos. Soc., arXiv:1206.3197], the authors established the general theory of Ulrich ideals and modules. While the classical version (maximally generated maximal Cohen-Macaulay modules) was introduced by B. Ulrich [Math. Z. 188, 23–32 (1984; Zbl 0573.13013)] and by Brennan-Herzog-Ulrich [J. P. Brennan et al., Math. Scand. 61, No. 2, 181–203 (1987; Zbl 0653.13015)], the notion of Ulrich modules is more general and describes a larger set. The broad goal is to classify all Ulrich ideals and modules. In the earlier paper the authors achieved this in the case of a one-dimensional Gorenstein local ring of finite CM-representation type. The main result of this paper is a classification of Ulrich ideals and Ulrich modules over two-dimensional Gorenstein rational singularities from a geometric point of view. To achieve this, the authors introduce and use the notion of weakly special Cohen-Macaulay modules. In the last section they consider two-dimensional non-Gorenstein rational singularities. Reviewer: Juan C. Migliore (Notre Dame) Cited in 1 ReviewCited in 11 Documents MSC: 13C14 Cohen-Macaulay modules 14B05 Singularities in algebraic geometry 14C25 Algebraic cycles 14E16 McKay correspondence Keywords:Ulrich ideals; rational singularities; maximal Cohen-Macaulay modules; Ulrich modules; ULrich ideals; Gorenstein local domains; weakly special Cohen-Macaulay modules Citations:Zbl 0573.13013; Zbl 0653.13015 PDFBibTeX XMLCite \textit{S. Goto} et al., Nagoya Math. J. 221, 69--110 (2016; Zbl 1360.13028) Full Text: DOI arXiv References: This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.