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Miller, Claudia ; Striuli, Janet ; Witt, Emily (Ed.)
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August, Jenny ; Cheung, Man Wai ; Faber, Eleonore ; Gratz, Sira ; Schroll, Sibylle ( , Journal of the London Mathematical Society)
Abstract We study a category of ‐graded maximal Cohen‐Macaulay (MCM) modules over the curve singularity and demonstrate that it has infinite type cluster combinatorics. In particular, we show that this Frobenius category (or a suitable subcategory) is stably equivalent to the infinite type cluster categories of Holm–Jørgensen, Fisher and Paquette–Yıldırım. As a consequence, has cluster tilting subcategories modelled by certain triangulations of the (completed) ‐gon. We use the Frobenius structure to extend this further to consider maximal almost rigid subcategories, and show that these subcategories and their mutations exhibit the combinatorics of the completed ‐gon.
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Faber, Eleonore ; Juhnke-Kubitzke, Martina ; Lindo, Haydee ; Miller, Claudia ; R. G., Rebecca ; Seceleanu, Alexandra ( , Association for Women in Mathematics series)Miller, Claudia ; Striuli, Janet ; Witt, Emily (Ed.)We generalize Buchsbaum and Eisenbud’s resolutions for the powers of the maximal ideal of a polynomial ring to resolve powers of the homogeneous maximal ideal over graded Koszul algebras.more » « less
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Faber, Eleonore ; Muller, Greg ; Smith, Karen E. ( , Advances in Mathematics)