Degenerations of the moduli spaces of vector bundles on curves I

Nagaraj, D. S.; Seshadri, C. S.

doi:10.1007/bf02837721

Cited by 43 publications

(65 citation statements)

References 9 publications

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“…There is Gieseker's construction [8], using bundles over semistable models for the nodal curve, in which the special fibre has non-smooth normal crossing singularities. Pandharipande [17] takes a different approach, involving torsion-free sheaves (see also Nagaraj-Seshadri [15]). …”

Section: Lemma 32 (A)mentioning

confidence: 99%

Lagrangian matching invariants for fibred four-manifolds: I

Perutz

2007

Geom. Topol.

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In a pair of papers, we construct invariants for smooth four-manifolds equipped with 'broken fibrations'-the singular Lefschetz fibrations of Auroux, Donaldson and Katzarkov-generalising the Donaldson-Smith invariants for Lefschetz fibrations.The 'Lagrangian matching invariants' are designed to be comparable with the SeibergWitten invariants of the underlying four-manifold; formal properties and first computations support the conjecture that equality holds. They fit into a field theory which assigns Floer homology groups to three-manifolds fibred over S 1 .The invariants are derived from moduli spaces of pseudo-holomorphic sections of relative Hilbert schemes of points on the fibres, subject to Lagrangian boundary conditions. Part I-the present paper-is devoted to the symplectic geometry of these Lagrangians.53D40, 57R57; 57R15

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Section: Lemma 32 (A)mentioning

confidence: 99%

Lagrangian matching invariants for fibred four-manifolds: I

Perutz

2007

Geom. Topol.

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“…This gives a proof of a conjecture by Seshadri and Nagaraj (Conjecture (a), p. 136 of [3]). Proving Seshadri-Nagaraj conjecture was not the aim of this note.…”

Section: Introductionmentioning

confidence: 55%

Vector bundles with a fixed determinant on an irreducible nodal curve

Bhosle

2005

Proc. Math. Sci.

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Abstract. Let M be the moduli space of generalized parabolic bundles (GPBs) of rank r and degree d on a smooth curve X. Let ML be the closure of its subset consisting of GPBs with fixed determinantL. We define a moduli functor for which ML is the coarse moduli scheme. Using the correspondence between GPBs on X and torsion-free sheaves on a nodal curve Y of which X is a desingularization, we show that ML can be regarded as the compactified moduli scheme of vector bundles on Y with fixed determinant. We get a natural scheme structure on the closure of the subset consisting of torsion-free sheaves with a fixed determinant in the moduli space of torsion-free sheaves on Y . The relation to Seshadri-Nagaraj conjecture is studied.

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“…This provided normal compactifications of the moduli spaces of vector bundles on singular curves. In a couple of interesting papers, degenerations of moduli spaces of vector bundles on curves were studied by Seshadri and Nagaraj [NagSes97], [NagSes99] generalising also results of Gieseker in rank 2. The classification of G-bundles on singular curves turned out to be much more difficult.…”

Section: Vector Bundles On Singular Curvesmentioning

confidence: 99%

Book Review: Collected papers of C. S. Seshadri. Volume 1. Vector bundles and invariant theory; Collected papers of C. S. Seshadri. Volume 2. Schubert geometry and representation Theory

Bhosle¹

2013

Bull. Amer. Math. Soc.

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Degenerations of the moduli spaces of vector bundles on curves I

Cited by 43 publications

References 9 publications

Lagrangian matching invariants for fibred four-manifolds: I

Lagrangian matching invariants for fibred four-manifolds: I

Vector bundles with a fixed determinant on an irreducible nodal curve

Book Review: Collected papers of C. S. Seshadri. Volume 1. Vector bundles and invariant theory; Collected papers of C. S. Seshadri. Volume 2. Schubert geometry and representation Theory

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