On the noncommutative Donaldson-Thomas invariants arising from brane tilings
type: Item
instance of: scholarly article
title: On the noncommutative Donaldson-Thomas invariants arising from brane tilings
zbMATH Open document ID: 1191.14008
author: Sergey Mozgovoy
author: Markus Reineke
published in: Advances in Mathematics
publication date: 2010-03-08T00:00:00Z
full work available at URL: https://arxiv.org/abs/0809.0117
review text: From the authors' abstract: ``Given a brane tiling, that is a bipartite graph on a torus, we can associate with it a quiver potential and a quiver potential algebra. Under certain consistency conditions on a brane tiling, we prove a formula for the Donaldson-Thomas type invariants of the moduli space of framed cyclic modules over the corresponding quiver potential algebra. We relate this formula with the counting of perfect matchings of the periodic plane tiling corresponding to the brane tiling. We prove that the same consistency conditions imply that the quiver potential algebra is a 3-Calabi-Yau algebra. We also formulate a rationality conjecture for the generating functions of the Donaldson-Thomas type invariants.''
reviewed by: Huang Hua-Lin
Mathematics Subject Classification ID: 14C05
Mathematics Subject Classification ID: 14J81
Mathematics Subject Classification ID: 16G70
zbMATH DE Number: 5678594
zbMATH Keywords: Hilbert scheme
zbMATH Keywords: brane tiling
zbMATH Keywords: quiver potential algebra
zbMATH Keywords: Donaldson-Thomas invariant
MaRDI profile type: Publication
OpenAlex ID: W2963462305
arXiv ID: 0809.0117
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DOI: 10.1016/J.AIM.2009.10.001
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description: scientific article