Ulrich ideals and modules over two-dimensional rational singularities (Q2828006)

In [``Ulrich ideals and modules,'' to appear in Math. Proc. Cambridge Philos. Soc., \url{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 \textit{B. Ulrich} [Math. Z. 188, 23--32 (1984; Zbl 0573.13013)] and by Brennan-Herzog-Ulrich [\textit{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.