Let C be a curve with two smooth components and a single node, and let "C(w, r, χ) be the moduli space of w-semistable classes of depth one sheaves on C having rank r on both components and Euler characteristic χ. In this paper, under suitable assumptions, we produce a projective bundle over the product of the moduli spaces of semistable vector bundles of rank r on each component and we show that it is birational to an irreducible component of "C(w, r, χ). Then we prove the rationality of the closed subset containing vector bundles with given fixed determinant.

Favale, F., Brivio, S. (2021). On vector bundles over reducible curves with a node. ADVANCES IN GEOMETRY, 21(3), 299-312 [10.1515/advgeom-2020-0010].

On vector bundles over reducible curves with a node

Favale, F;Brivio, S
2021

Abstract

Let C be a curve with two smooth components and a single node, and let "C(w, r, χ) be the moduli space of w-semistable classes of depth one sheaves on C having rank r on both components and Euler characteristic χ. In this paper, under suitable assumptions, we produce a projective bundle over the product of the moduli spaces of semistable vector bundles of rank r on each component and we show that it is birational to an irreducible component of "C(w, r, χ). Then we prove the rationality of the closed subset containing vector bundles with given fixed determinant.
Articolo in rivista - Articolo scientifico
nodal curves; Stability; vector bundles;
English
26-lug-2020
2021
21
3
299
312
open
Favale, F., Brivio, S. (2021). On vector bundles over reducible curves with a node. ADVANCES IN GEOMETRY, 21(3), 299-312 [10.1515/advgeom-2020-0010].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/254370
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