The intrinsic normal cone

Behrend, Kai; Fantechi, Barbara

doi:10.1007/s002220050136

Cited by 724 publications

(1,238 citation statements)

References 12 publications

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“…they carry natural perfect obstruction theories [52,7]. Similar results have been previously obtained for moduli spaces of (decorated) sheaves in [80,66,56,70].…”

Section: Virtual Smoothness For Adhm Sheaves On Curvessupporting

confidence: 78%

“…However the later disallows all proper subsheaves E ′ ⊂ E satisfying the conditions listed there, not only the saturated ones. It will become clear in section (7) that this difference has important consequences for the connection to local DonaldsonThomas theory.…”

Section: Remark 12 (I)mentioning

confidence: 99%

“…Although the construction presented in [70] is based on the formalism of [7], it is fairly straightforward to provide an alternative construction of a perfect tangent-obstruction theory of M St (Y, d, n) For future reference, let us recall the construction of tangent and respectively obstruction spaces, according to [80,Sect 3], [70,Sect 2]. Given a flat family (Q S , ρ S ) of stable pairs, let C(Q S , ρ S ) denote the two term complex of O Y S -modules…”

Section: Admissible Pairsmentioning

confidence: 99%

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Moduli of ADHM sheaves and the local Donaldson–Thomas theory

Diaconescu

2012

Journal of Geometry and Physics

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Abstract. The ADHM construction establishes a one-to-one correspondence between framed torsion free sheaves on the projective plane and stable framed representations of a quiver with relations in the category of complex vector spaces. This paper studies the geometry of moduli spaces of representations of the same quiver with relations in the abelian category of coherent sheaves on a smooth complex projective curve X. In particular it is proven that this moduli space is virtually smooth and related by relative Beilinson spectral sequence to the curve counting construction via stable pairs of Pandharipande and Thomas. This yields a new conjectural construction for the local Donaldson-Thomas theory of curves as well as a natural higher rank generalization.

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“…they carry natural perfect obstruction theories [52,7]. Similar results have been previously obtained for moduli spaces of (decorated) sheaves in [80,66,56,70].…”

Section: Virtual Smoothness For Adhm Sheaves On Curvessupporting

confidence: 78%

Section: Remark 12 (I)mentioning

confidence: 99%

Section: Admissible Pairsmentioning

confidence: 99%

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Moduli of ADHM sheaves and the local Donaldson–Thomas theory

Diaconescu

2012

Journal of Geometry and Physics

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“…In [101] we describe the moduli spaces M γ (n, k) whose contributions dominate the gauge theory path integral, explicitly, via modified ADHM construction. More precisely, the gauge theory path integral localizes to the integral of 1 over the virtual fundamental cycle of degree (dimension) zero M γ (n, k) which is represented, in the perfect obstruction theory language of [11] by a smooth (super)-variety M γ (n, k) c (c stands for coarse) and H-equivariant vector bundle Obs γ → M γ (n, k) c . The k-instanton contribution to the gauge theory partition function is the Euler class…”

Section: Integration Over Instanton Moduli Spacesmentioning

confidence: 99%

BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters

Nekrasov

2016

J. High Energ. Phys.

213

466

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We study symmetries of quantum field theories involving topologically distinct sectors of the field space. To exhibit these symmetries we define special gauge invariant observables, which we call the qq-characters. In the context of the BPS/CFT correspondence, using these observables, we derive an infinite set of Dyson-Schwinger-type relations. These relations imply that the supersymmetric partition functions in the presence of Ω-deformation and defects obey the Ward identities of two dimensional conformal field theory and its q-deformations. The details will be discussed in the companion papers.

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“…A virtual cycle is then obtained by [4,22]. The resulting invariants P n,β = [P n (X,β)] vir 1 are conjecturally equal to the reduced DT invariants of [23].…”

Section: Introductionmentioning

confidence: 99%

Stable pairs and BPS invariants

Pandharipande

Thomas

2009

J. Amer. Math. Soc.

155

179

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We define the BPS invariants of Gopakumar-Vafa in the case of irreducible curve classes on Calabi-Yau 3-folds. The main tools are the theory of stable pairs in the derived category and Behrend's constructible function approach to the virtual class. We prove that for irreducible classes the stable pairs generating function satisfies the strong BPS rationality conjectures. We define the contribution of each curve to the BPS invariants. A curve $C$ only contributes to the BPS invariants in genera lying between the geometric genus and arithmetic genus of $C$. Complete formulae are derived for nonsingular and nodal curves. A discussion of primitive classes on K3 surfaces from the point of view of stable pairs is given in the Appendix via calculations of Kawai-Yoshioka. A proof of the Yau-Zaslow formula for rational curve counts is obtained. A connection is made to the Katz-Klemm-Vafa formula for BPS counts in all genera.Comment: Fixed typo pointed out by Filippo Vivian

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The intrinsic normal cone

Abstract: We suggest a construction of virtual fundamental classes of certain types of moduli spaces.Comment: LaTeX, Postscript file available at http://www.math.ubc.ca/people/faculty/behrend/inc.p

Cited by 724 publications

References 12 publications

Moduli of ADHM sheaves and the local Donaldson–Thomas theory

Moduli of ADHM sheaves and the local Donaldson–Thomas theory

BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters

Stable pairs and BPS invariants

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