Moses Kim | Searcharxiv

arXiv2020

Infinitesimal semi-invariant pictures and co-amalgamation

The purpose of this paper is to study the local structure of the semi-invariant picture of a tame hereditary algebra near the null root. Using a construction that we call co-amalgamation, we show that this local structure is completely described by the semi-invariant pictures of a collection of self-injective Nakayama algebras. We then describe the cones of this local structure using cluster-like structures that we call support regular clusters. Finally, we show that the local structure is (piecewise linearly) invariant under cluster tilting.

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arXiv2018

Weighted quivers

A "weight" on a quiver $Q$ with values in a group $G$ is a function which assigns an element of $G$ for each arrow in $Q$. This paper shows that the essential steps in the mutation of quivers with potential [DWZ] goes through with weights provided that the weights on each cycle in the potential have trivial product. This gives another proof of the sign coherence of $c$-vectors. We also classify all weights on tame quivers.

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