A refined Brill–Noether theory over Hurwitz spaces

2019/07/19 by Hannah K. Larson, Hannah Larson, Larson, Hannah K. · 4 citations
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #Commutative Algebra and Its Applications

paper · doi:10.1007/s00222-020-01023-z

Abstract

Let f\colon C → ℙ¹ be a degree k genus g cover. The stratification of line bundles L ∈ Pic^d(C) by the splitting type of f_*L is a refinement of the stratification by Brill-Noether loci W^r_d(C). We prove that for general degree k covers, these strata are smooth of the expected dimension. In particular, this determines the dimensions of all irreducible components of W^r_d(C) for a general k-gonal curve (there are often components of different dimensions), extending results of Pflueger and Jensen-Ranganathan. The results here apply over any algebraically closed field.

Citations

• Stable curves and special divisors: Petri's conjecture

Cited by

• Smoothness results for the schemes of special divisors on general k-gonal curves
• When are splitting loci Gorenstein?
• Brill--Noether loci in genus ≤ 12
• Resolving the Singularities of Splitting Loci
• Universal degeneracy classes for vector bundles on ℙ¹ bundles