English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

A line bundle on a smooth curve $C$ with two marked points determines a rankfunction $r(a,b) = h^0(C, L(-ap-bq))$. This paper studies Brill-Noetherdegeneracy loci; such a locus is defined to be the closure in$\operatorname{Pic}^d(C)$ of the locus of line bundles with a specified rankfunction. These loci generalize the classical Brill-Noether loci $W^r_d(C)$ aswell as Brill-Noether loci with imposed ramification. For general $(C,p,q)$ wedetermine the dimension, singular locus, and intersection class ofBrill-Noether degeneracy loci, generalizing classical results about $W^r_d(C)$.The intersection class has a combinatorial interpretation in terms of thenumber of reduced words for a permutation associated to the rank function, oralternatively the number of saturated chains in the Bruhat order. The essentialtool is a versality theorem for a certain pair of flags on$\operatorname{Pic}^d(C)$, conjectured by Melody Chan and the author. We provethis versality theorem by showing the injectivity of a generalized Petri map,along the lines of Eisenbud and Harris's proof of the Gieseker-Petri theorem.

Versality of Brill-Noether flags and degeneracy loci of twice-marked curves