Brill-Noether locus of rank 1 and degree g-1 on a nodal curve

Details Brill-Noether locus of rank 1 and degree g-1 on a nodal curve Brill-Noether locus of rank 1 and degree g-1 on a nodal curve

2011-09-27

arxiv.org/abs/1109.5926v1

Mathematics

Algebraic Geometry

16 pages. comments welcome!

Scientific paper

In this paper we consider the Brill-Noether locus $W_{\underline d}(C)$ of line bundles of multidegree $\underline d$ of total degree $g-1$ having a nonzero section on a nodal reducible curve $C$ of genus $g\geq2$. We give an explicit description of the irreducible components of $W_{\underline d}(C)$ for a semistable multidegre $\underline d$. As a consequence we show that, if two semistable multidegrees of total degre $g-1$ on a curve with no rational components differ by a twister, then the respective Brill-Noether loci have isomorphic components.

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