A refined Brill-Noether theory over Hurwitz spaces

• 成果类型: Article
• 署名作者: Larson, Hannah K.
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-020-01023-z
• 发表日期: 2021
• 页码: 767-790
• 关键词: linear series; PROOF; VARIETIES; EXISTENCE

摘要

Let f : C -> P-1 be a degree k genus g cover. The stratification of line bundles L is an element of Pic(d) (C) by the splitting type of f(*)L is a refinement of the stratification by Brill-Noether loci W-d(r) (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-d(r)(C) for a general k-gonal curve (there are often components of different dimensions), extending results of Pflueger (Adv Math 312:46-63, 2017) and Jensen and Ranganathan (Brill-Noether theory for curves of a fixed gonality, arXiv:1701.06579, 2017). The results here apply over any algebraically closed field.