Geometric model for syzygies over certain 2-Calabi-Yau tilted algebras
Khrystyna Serhiyenko (University of Kentucky)
Wednesday 4th November, 2020 16:00-17:00 online (zoom)
A module is said to be a syzygy if it is a submodule of a projective. In the case of 2-Calabi-Yau (2-CY) tilted algebras the non-projective syzygies form a triangulated 3-CY category. In this setting, the category of syzygies is equivalent to the category of Cohen-Macauley modules and also the singularity category of the algebra. We find a geometric model for this category for a particular type of 2-CY tilted algebras given by quivers with relations. More precisely, we construct a decorated polygon with a checkerboard pattern whose 2-diagonals correspond to syzygies. Moreover, other aspects of the syzygy category such as morphisms, extensions, Auslander-Reiten triangles, and the shift also have a geometric interpretation in this polygon. This is joint work with Ralf Schiffler.