In this paper, we deal with Brill-Noether theory for higher-rank sheaves on a polarized nodal reducible curve (C,w̲) following the ideas of Brambila-Paz et al. (J Algebraic Geom 6(4): 645–669, 1997). We study the Brill-Noether loci of w̲-stable depth one sheaves on C having rank r on all irreducible components and having small slope. In analogy with what happens in the smooth case, we prove that these loci are closely related to BGN extensions. Moreover, we produce irreducible components of the expected dimension for these Brill-Noether loci.

Brivio, S., Favale, F. (2023). Higher-rank Brill-Noether loci on nodal reducible curves. GEOMETRIAE DEDICATA, 217(2 (April 2023)), 1-23 [10.1007/s10711-023-00767-1].

Higher-rank Brill-Noether loci on nodal reducible curves

Brivio, S
;
Favale, FF
2023

Abstract

In this paper, we deal with Brill-Noether theory for higher-rank sheaves on a polarized nodal reducible curve (C,w̲) following the ideas of Brambila-Paz et al. (J Algebraic Geom 6(4): 645–669, 1997). We study the Brill-Noether loci of w̲-stable depth one sheaves on C having rank r on all irreducible components and having small slope. In analogy with what happens in the smooth case, we prove that these loci are closely related to BGN extensions. Moreover, we produce irreducible components of the expected dimension for these Brill-Noether loci.
Articolo in rivista - Articolo scientifico
Brill-Noether loci; Moduli spaces; Nodal curves; Polarizations; Stability;
English
28-gen-2023
2023
217
2 (April 2023)
1
23
35
open
Brivio, S., Favale, F. (2023). Higher-rank Brill-Noether loci on nodal reducible curves. GEOMETRIAE DEDICATA, 217(2 (April 2023)), 1-23 [10.1007/s10711-023-00767-1].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/403664
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