Affiliation:
1. Department of Mathematics Aarhus University Aarhus C Denmark
2. School of Mathematics, Kavli IPMU (WPI) UTIAS, The University of Tokyo Chiba Japan
3. School of Mathematics University of Leeds Leeds UK
4. Department of Mathematics Universität zu Köln Köln Germany
5. Department of Mathematical Sciences Norwegian University of Science and Technology Trondheim Norway
Abstract
AbstractWe 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.
Funder
London Mathematical Society
National Science Foundation
Association for Women in Mathematics
Alfred P. Sloan Foundation
Villum Fonden
Danmarks Grundforskningsfond
Ministry of Education, Culture, Sports, Science and Technology
Engineering and Physical Sciences Research Council
University Of Leeds