A picture of the irreducible components of W^r_d(C) for a general k-gonal curve C

2025/04/29 by Marc Coppens, Coppens, Marc · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Geometry and complex manifolds

paper · doi:10.48550/arxiv.2504.21141

Abstract

Based on results on Hurwitz-Brill-Noether theory obtained by H. Larson we give a picture of the irreducible components of W^r_d(C) for a general k-gonal curve of genus g. This picture starts from irreducible components of W^r_d(C) restricted to an open subset of Pic (C) satisfying Brill-Noether theory as in the case of a general curve of genus g. We obtain some degeneracy loci associated to a morphism of locally-free sheaves on them of the expected dimension. All the irreducible components of the schemes W^r_d(C) are translates of their closures in Pic (C). We complete the proof that the schemes W^r_d(C) are generically smooth in case C is a general k-gonal curve (claimed but not completely proved before). We obtain some results on the tangent spaces to the splitting degeneracy loci for an arbitrary k-gonal curve and we obtain some new smoothness results in case C is a general k-gonal curve.

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• Resolving the Singularities of Splitting Loci

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