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2008 Non-commutative Donaldson–Thomas invariants and the conifold
Balázs Szendrői
Geom. Topol. 12(2): 1171-1202 (2008). DOI: 10.2140/gt.2008.12.1171


Given a quiver algebra A with relations defined by a superpotential, this paper defines a set of invariants of A counting framed cyclic A–modules, analogous to rank–1 Donaldson–Thomas invariants of Calabi–Yau threefolds. For the special case when A is the non-commutative crepant resolution of the threefold ordinary double point, it is proved using torus localization that the invariants count certain pyramid-shaped partition-like configurations, or equivalently infinite dimer configurations in the square dimer model with a fixed boundary condition. The resulting partition function admits an infinite product expansion, which factorizes into the rank–1 Donaldson–Thomas partition functions of the commutative crepant resolution of the singularity and its flop. The different partition functions are speculatively interpreted as counting stable objects in the derived category of A–modules under different stability conditions; their relationship should then be an instance of wall crossing in the space of stability conditions on this triangulated category.


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Balázs Szendrői. "Non-commutative Donaldson–Thomas invariants and the conifold." Geom. Topol. 12 (2) 1171 - 1202, 2008.


Received: 24 July 2007; Revised: 9 January 2008; Accepted: 7 February 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1143.14034
MathSciNet: MR2403807
Digital Object Identifier: 10.2140/gt.2008.12.1171

Primary: 14J32
Secondary: 14N10

Rights: Copyright © 2008 Mathematical Sciences Publishers


Vol.12 • No. 2 • 2008
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