Neutral linear series and Brill-Noether theory of singular curves

Abstract

On a projective nonsingular curve C of genus g the variety Nr n(A) of neutral linear series parameterizes linear series of degree n and dimension r to which a given effective divisor A of degree s does not impose independent conditions. Edoardo Sernesi proved that, in the appropriate ranges of g, r, n, s, if C is a Brill-Noether curve then Nr n(A) is non-empty. As an application, here we deduce a Brill-Noether existence theorem for irreducible curves obtained from a Brill-Noether curve by identifying a pair of points to an ordinary node.

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