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.
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