Torsion-free sheaves on nodal curves and triples

Avritzer, Dan; Lange, Herbert; Ribeiro, Flaviana Andrea

doi:10.1007/s00574-010-0020-1

Cited by 4 publications

(4 citation statements)

References 8 publications

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“…This follows when C has a node at z from Propositions (2) and (3) of chapter (8) of [Ses82]. When C has a cusp at z, the statement follows from the main theorem of [ARM12]. Because of its structure, a deformation of E z may be given by merely deforming m z .…”

Section: Git Construction Of the Compactified Universal Moduli Spacementioning

confidence: 94%

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Compactifications of Universal Moduli Spaces of Vector Bundles and the Log-Minimal Model Program on $\overline{M}_{g}$

Grimes

2018

International Mathematics Research Notices

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Recent work on the log-minimal model program for the moduli space of curves, as well as past results of Caporaso, Pandharipande, and Simpson motivate an investigation of compactifications of the universal moduli space of slope semi-stable vector bundles over moduli spaces of curves arising in the Hassett-Keel program. Our main result is the construction of a compactification of the universal moduli space of vector bundles over several of these moduli spaces, along with a complete description in the case of pseudo-stable curves.Theorem 1.0.1. For all α ∈ Q ∩ (2/3, 1], e, r ≥ 1 and g ≥ 3, there exists a projective variety U e,r,g (α) with a canonical projection π : U e,r,g (α) → M g (α) such that the diagram U e,r (C • g /M • g ) / / U e,r,g (α)

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Section: Git Construction Of the Compactified Universal Moduli Spacementioning

confidence: 94%

“…where a z is an integer determined by E called the local semirank of E (see [ARM12]). This follows when C has a node at z from Propositions (2) and (3) of chapter (8) of [Ses82].…”

Section: Git Construction Of the Compactified Universal Moduli Spacementioning

confidence: 99%

Compactifications of Universal Moduli Spaces of Vector Bundles and the Log-Minimal Model Program on $\overline{M}_{g}$

Grimes

2018

International Mathematics Research Notices

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“…Then K d is an even lattice of signature (1,4). There exists a K3 surface Y K d with P ic(Y K d ) ≃ K d , and such that the classes {A, B, Γ 1 , Γ 2 , Γ 3 } are all represented by nodal, reduced curves such that the nodal curve A meets Γ 1 , Γ 2 and Γ 3 transversally.…”

Section: Generic Finiteness Of the Morphism ηmentioning

confidence: 99%

“…2.3]. 4 Lemma 3.3. Let f ∶ B → X be an unramified morphism from a connected nodal curve to a K3 surface, and let N f denote the normal bundle of f .…”

Section: Generic Finiteness Of the Morphism ηmentioning

confidence: 99%

The moduli of singular curves on K3 surfaces

Kemeny

2015

Journal de Mathématiques Pures et Appliquées

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In this article we consider moduli properties of singular curves on K3 surfaces. Let B g denote the stack of primitively polarized K3 surfaces (X, L) of genus g and let T n g,k → B g be the stack parametrizing tuples [(f ∶ C → X, L)] with f an unramified morphism which is birational onto its image, C a smooth curve of genus p(g, k) − n and f * C ∈ kL . We show that the forgetful morphismis generically finite on at least one component, for all but finitely many values of p(g, k) − n. We further study the Brill-Noether theory of those curves parametrized by the image of η, and find a Wahl-type obstruction for a smooth curve with an unordered marking to have a nodal model on a K3 surface in such a way that the marking is the divisor over the nodes.

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Generalized parabolic structures over smooth curves with many components and principal bundles over reducible nodal curves

Castañeda

2022

Annali di Matematica

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Torsion-free sheaves on nodal curves and triples

Abstract: We study torsion free sheaves on integral projective curves with at most ordinary cusps as singularities. Adjusting Seshadri's structure from the nodal case to this one, we describe these sheaves by means of a triple defined in the normalization of the curve.Pi 1

Cited by 4 publications

References 8 publications

Compactifications of Universal Moduli Spaces of Vector Bundles and the Log-Minimal Model Program on $\overline{M}_{g}$

Compactifications of Universal Moduli Spaces of Vector Bundles and the Log-Minimal Model Program on $\overline{M}_{g}$

The moduli of singular curves on K3 surfaces

Generalized parabolic structures over smooth curves with many components and principal bundles over reducible nodal curves

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