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Grassmannian cluster structures and line singularities

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If you have a question about this talk, please contact Matthew Westaway.

This talk is about a categorification of the coordinate rings of Grassmannians of infinite rank in terms of graded maximal Cohen-Macaulay modules over the commutative ring ℂ[x,y]/(xk). This yields an infinite rank analogue of the Grassmannian cluster categories introduced by Jensen, King, and Su. In the special case k=2, Spec(ℂ[x,y]/(x2)) is a type A-curve singularity and the ungraded version of our category has been studied by Buchweitz, Greuel, and Schreyer in the 1980s. We show that this Frobenius category has infinite type A cluster combinatorics, in particular, that it has cluster-tilting subcategories modelled by certain triangulations of the (completed) infinity-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 infinity-gon. This is joint work with Jenny August, Man-Wai Cheung, Sira Gratz, and Sibylle Schroll.

This talk is part of the Algebra Seminar series.

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