Denseness of g-vector fans for tame algebras

2021/01/07 木 10:30 - 12:00
Toshiya Yurikusa
Tohoku University

The g-vector fan of a finite dimensional algebra is a simplicial polyhedral
fan whose rays are the g-vectors of the indecomposable 2-term presilting
complexes. We consider the property that the g-vector fan is dense. We
prove that gentle algebras satisfy it by using their surface model (based
on a joint work with Toshitaka Aoki). The main ingredients of our proof are
the g-vectors of the laminations and their asymptotic behavior under Dehn
twists. More generally, using the generic decompositions and twist functors
instead of them, we can prove it for tame algebras (based on a joint work
with Pierre-Guy Plamondon).


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