Donaldson-Thomas type invariants via microlocal geometry

By K. Behrend. 2009

288 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9709467133ae815907a2c8521f7caa65ebc4d371

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Refined stable pair invariants for E-, M- and [p, q]-strings (2013, background): “e pairs is denoted P n(M;). Stable pairs on CalabiYau threefolds have a perfect and symmetric obstruction theory, which follows from Serre duality and the triviality of the canonical class, see e.g. [48]. A symmetric obstruction theory implies that the rst order deformations Ext1(I;I) are dual to th”
Symmetries and stabilization for sheaves of vanishing cycles (2012, background): “In [4, §5.3], Behrend and Fantechi discuss how to define a ‘Fukaya category’ using their ideas.”
Localizing virtual cycles by cosections (2010, unknown): “From the distinguished triangle π∗ SL • S −→ LM −→ LM/S −→ π∗ SLS [1] = [π∗ SΩS → 0],”
Hall algebras and curve-counting invariants (2010, background): “Recall [1] that Behrend defined for every scheme S of finite type over C a constructible function νS : S → Z, with the property that when f : T → S is a smooth morphism of relative dimension d, there is an identity (6) νT = (−1)f(νS).”
A Darboux theorem for derived schemes with shifted symplectic structure (2013, unknown): “Deﬁne a cdga A (2) whose underlying commutative graded algebra is free over A (1) with generators given by M − 2 in degree − 2 and with diﬀerential d determined by the map π − 2 : M − 2 [1] → A (1).”
Deformation-obstruction theory for complexes via Atiyah and Kodaira–Spencer classes (2008, methodology): “Applied to E this induces the adjunction i ∗ i∗(E0 ⊗ I )[1] E0 ⊗ I [ 1 ], where E0 = i ∗ E. But by construction it is the pushforward by h∗ of the second arrow of (3.2), and”
A classical model for derived critical loci (2013, methodology): “Following Behrend [2], we call φ : E• → LX a symmetric obstruction theory if we also are given an isomorphism θ : E• → E•∨[1] with θ∨[1] = θ.”
Categorification of Donaldson-Thomas invariants via Perverse Sheaves (2012, methodology): “1) RΓ{Re q≤0}Q→ Q→ Rı∗ı Q where ı : {Re q > 0} →֒ C is the inclusion, we find that Aq [1] is a sheaf complex supported at the origin satisfying A[1] ∼= Q[−r + 1], i.”
A theory of generalized Donaldson–Thomas invariants (2008, methodology): “They were introduced by Behrend [3] for finite type C-schemes X ; the generalization to Artin stacks in §4.”