GLSMs for partial flag manifolds

Donagi, Ron; Sharpe, Eric

doi:10.1016/j.geomphys.2008.07.010

Cited by 56 publications

(77 citation statements)

References 36 publications

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“…This is analogous to the similar statement concerning Quot schemes parameterizing coherent quotients on P 1 and holomorphic maps to the Grassmannian [12,10]. Note that the later have been shown to occur in a similar context in [26,38]. A renormalization group flow analogous to [57,39] yields a conjectural relation between the residual ADHM invariants defined in this paper and the J-function of the moduli space of framed torsion-free sheaves generalizing the results of [53,17,10,11] for J-functions of Grassmannians and flag varieties.…”

supporting

confidence: 76%

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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supporting

confidence: 76%

Moduli of ADHM sheaves and the local Donaldson–Thomas theory

Diaconescu

2012

Journal of Geometry and Physics

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“…In [6], further nonabelian examples were presented, expanding on that discussed in [3][section 5], and the relevance of homological projective duality, discussed in more detail in this paper, was introduced.…”

Section: Contents 1 Introduction 4 1 Introductionmentioning

confidence: 99%

Non-Birational Twisted Derived Equivalences in Abelian GLSMs

Căldăraru

Distler

Hellerman

et al. 2009

Commun. Math. Phys.

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178

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In this paper we discuss some examples of abelian gauged linear sigma models realizing twisted derived equivalences between non-birational spaces, and realizing geometries in novel fashions. Examples of gauged linear sigma models with non-birational Kähler phases are a relatively new phenomenon. Most of our examples involve gauged linear sigma models for complete intersections of quadric hypersurfaces, though we also discuss some more general cases and their interpretation. We also propose a more general understanding of the relationship between Kähler phases of gauged linear sigma models, namely that they are related by (and realize) Kuznetsov's 'homological projective duality.' Along the way, we shall see how 'noncommutative spaces' (in Kontsevich's sense) are realized physically in gauged linear sigma models, providing examples of new types of conformal field theories. Throughout, the physical realization of stacks plays a key role in interpreting physical structures appearing in GLSMs, and we find that stacks are implicitly much more common in GLSMs than previously realized.

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“…[8] and references therein). These moduli spaces arise physically in "gauged linear sigma models," thus the name.…”

Section: Topological Field Theories and The A/2 B/2 Modelsmentioning

confidence: 99%