On two examples by Iyama and Yoshino

By B. Keller, Daniel Murfet, Michel van den Bergh. Compositio Mathematica, 2008

104 citations recorded by the source corpus.

Abstract In a recent paper, Iyama and Yoshino considered two interesting examples of isolated singularities over which it is possible to classify the indecomposable maximal Cohen–Macaulay modules in terms of linear algebra data. In this paper, we present two new approaches to these examples. In the first approach we give a relation with cluster categories. In the second approach we use Orlov’s result on the graded singularity category.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/58b3369a0fd9a79f5d423d66fd1bdfbb84bf6dc7

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In Algebra and Number Theory

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Citations in the corpus

Strong generators in $D^{perf}(X)$ and $D^b_{coh}(X)$ (2017, background): “2] generalized to separated schemes of finite type over arbitrary fields, but this Proposition disappeared in the passage to the published version [22].”
Compact generators in categories of matrix factorizations (2009, unknown): “ut relations to previous work. I thank Daniel Murfet for informing me that Corollary 4.2(1) was ﬁrst proven by Schoutens in [Sch03]. An independent proof by Murfet will be contained as an appendix in [KVdB08]. It is also possible to deduce the statement using results from [Orl09] as explained in [Se”
Classifying thick subcategories of the stable category of Cohen-Macaulay modules (2009, background): “en-Macaulay modules which are free on the punctured spectrum over a Cohen-Macaulay local ring Rand its completion Rb. The second assertion includes a recent result of Keller, Murfet and Van den Bergh [42], and a theorem of Leuschke and Wiegand [56, 45]. Theorem C. Let Rbe a Cohen-Macaulay local ring”
A category of kernels for equivariant factorizations and its implications for Hodge theory (2011, methodology): “. .. . .. . .. . .. . zd−1 zd−1 zd−1 ··· zd−1 which gives HH0(MF(k[x],xd,Z)) = kand HHi(MF(k[x],xd,Z)) = 0 for i6= 0, as expected. The Serre functor for MF(k[x],xd,Z) is (1 −d)[−1] (see [KMV08]). Computing the morphism space, HomMF(k[x,y],xd−yd,Z⊟Z)(∆,S), gives 0 Ld−1 i=0 k(−i,i) Ld−1 i=0 kz ”
Orlov spectra: bounds and gaps (2010, background): “This lemma was first noted in [28] as Lemma 5.”