Deformations of the Moduli Space of Vector Bundles Over an Algebraic Curve

Narasimhan, M. S.; Ramanan, S.

doi:10.2307/1970933

Cited by 167 publications

(157 citation statements)

References 12 publications

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“…As in Laszlo [14] (see also Narasimhan-Ramanan [17] and Pauly [21]), we can find an étale affine neighbourhood S = Spec(A) of E in U and a family of stable vector bundles E over S × X such that for each F ∈ S, we have E| {F }×X ∼ = F , together with a homomorphism μ: M → N of flat A-modules of finite type such that for all A-modules P , by functoriality,…”

Section: Phmentioning

confidence: 85%

Geometry of Vector Bundle Extensions and Applications to a Generalised Theta Divisor

Hitching¹

2013

MATH. SCAND.

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Let E and F be vector bundles over a complex projective smooth curve X, and suppose that 0 → E → W → F → 0 is a nontrivial extension. Let G ⊆ F be a subbundle and D an effective divisor on X. We give a criterion for the subsheaf G(−D) ⊂ F to lift to W , in terms of the geometry of a scroll in the extension space PH 1 (X, Hom(F, E)). We use this criterion to describe the tangent cone to the generalised theta divisor on the moduli space of semistable bundles of rank r and slope g − 1 over X, at a stable point. This gives a generalisation of a case of the Riemann-Kempf singularity theorem for line bundles over X. In the same vein, we generalise the geometric Riemann-Roch theorem to vector bundles of slope g − 1 and arbitrary rank.

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Section: Phmentioning

confidence: 85%

Geometry of Vector Bundle Extensions and Applications to a Generalised Theta Divisor

Hitching¹

2013

MATH. SCAND.

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“…It is stated in [3] that it can be easily deduced from the results of that paper that the map X → M 0 is also injective. This would imply that the curve X can be identified with M 0 .…”

Section: Introductionmentioning

confidence: 90%

“…The bundles U x were shown to be semistable in [1, Proposition 2.4], but the proof does not seem to imply stability directly, even though we know also by [3] that U x is simple.…”

Section: Stability Of U Xmentioning

confidence: 99%

On Poincaré bundles of vector bundles on curves

Lange

Newstead

2005

manuscripta math.

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“…For some other references on this subject, see [1,2,3,4,5,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,28,29,30,31,33,35,36,37].…”

Section: Theorem 12 ([7]mentioning

confidence: 99%

Geometry of the intersection ring and vanishing relations in the cohomology of the moduli space of parabolic bundles on a curve

Gamse¹,

Weitsman²

2016

J. Differential Geom.

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Abstract. We study the ring generated by the Chern classes of tautological line bundles on the moduli space of parabolic bundles of arbitrary rank on a Riemann surface. We show the Poincaré duals to these Chern classes have simple geometric representatives. We use this construction to show that the ring generated by these Chern classes vanishes below the dimension of the moduli space, in analogy with the Newstead-Ramanan conjecture for stable bundles.

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Deformations of the Moduli Space of Vector Bundles Over an Algebraic Curve

Cited by 167 publications

References 12 publications

Geometry of Vector Bundle Extensions and Applications to a Generalised Theta Divisor

Geometry of Vector Bundle Extensions and Applications to a Generalised Theta Divisor

On Poincaré bundles of vector bundles on curves

Geometry of the intersection ring and vanishing relations in the cohomology of the moduli space of parabolic bundles on a curve

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