Bridgeland stability conditions on the acyclic triangular quiver
type: Item
instance of: scholarly article
title: Bridgeland stability conditions on the acyclic triangular quiver
zbMATH Open document ID: 1423.16013
author: G. Dimitrov
author: Ludmil Katzarkov
published in: Advances in Mathematics
publication date: 2015-12-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/1410.0904
review text: Let $k$ be an algebraically closed field, let $Q$ be the only affine acyclic quiver with three vertices, $\mathrm{Rep}_k(Q)$ -- the category of $k$-representations of $Q$ and $D^b(\mathrm{Rep}_k(Q)$ -- the derived category of $\mathrm{Rep}_k(Q)$. The authors prove that the space of Bridgeland stability conditions $\mathrm{Stab}(D^b(\mathrm{Rep}_k(Q)))$ is a contractible (in particular connected) manifold. This is the first example of quiver $Q$ (different from Dynkin and Kronecker quivers) with this property. To prove the main theorem the authors develop their previous results presented in ``Non-semistable exceptional objects in hereditary categories''. The motivation for this research is its connection with homological mirror symmetry.
reviewed by: Justyna Kosakowska
Mathematics Subject Classification ID: 16G20
Mathematics Subject Classification ID: 16E35
zbMATH DE Number: 6523786
zbMATH Keywords: Bridgeland stability conditions on triangulated categories
zbMATH Keywords: exceptional collections
zbMATH Keywords: tame representation type quiver
zbMATH Keywords: affine quiver
zbMATH Keywords: contractible space
MaRDI profile type: Publication
OpenAlex ID: W2963353540
arXiv ID: 1410.0904
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DOI: 10.1016/J.AIM.2015.10.014
description: scientific article