Non-commutative Donaldson-Thomas theory and the conifold

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dc.creatorSzendroi, Balazs
dc.date2007-05-23
dc.date2008-09-19
dc.date.accessioned2026-07-07T10:15:58Z
dc.date.available2026-07-07T10:15:58Z
dc.descriptionGiven 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.
dc.descriptionInfinite product form, conjectured in v1, now a theorem of Ben Young. Additional discussion of small-volume expansion related to Eisenstein-like series
dc.identifierhttps://arxiv.org/abs/0705.3419
dc.identifierhttp://arxiv.org/abs/0705.3419
dc.identifierGeom.Topol.12:1171-1202,2008
dc.identifierdoi:10.2140/gt.2008.12.1171
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173353
dc.subjectAlgebraic Geometry
dc.subjectHigh Energy Physics - Theory
dc.titleNon-commutative Donaldson-Thomas theory and the conifold
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