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.

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