Higher-rank Brill-Noether loci on nodal reducible curves

Abstract

In this paper, we deal with Brill-Noether theory for higher-rank sheaves on a polarized nodal reducible curve (C,{{,mathrm{underline{w}},}}) following the ideas of Brambila-Paz et al. (J Algebraic Geom 6(4): 645–669, 1997). We study the Brill-Noether loci of {{,mathrm{underline{w}},}}-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.