#### Title

K-Classes Of Brill–Noether Loci And A Determinantal Formula

#### Document Type

Article

#### Publication Date

4-26-2021

#### Published In

International Mathematics Research Notices

#### Abstract

We compute the Euler characteristic of the structure sheaf of the Brill–Noether locus of linear series with special vanishing at up to two marked points. When the Brill–Noether number ρ is zero, we recover the Castelnuovo formula for the number of special linear series on a general curve; when ρ=1, we recover the formulas of Eisenbud-Harris, Pirola, and Chan–Martín–Pflueger–Teixidor for the arithmetic genus of a Brill–Noether curve of special divisors. These computations are obtained as applications of a new determinantal formula for the K-theory class of certain degeneracy loci. Our degeneracy locus formula also specializes to new determinantal expressions for the double Grothendieck polynomials corresponding to 321-avoiding permutations and gives double versions of the flagged skew Grothendieck polynomials recently introduced by Matsumura. Our result extends the formula of Billey–Jockusch–Stanley expressing Schubert polynomials for 321-avoiding permutations as generating functions for flagged skew tableaux.

#### Recommended Citation

D. Anderson, Linda Chen, and N. Tarasca.
(2021).
"K-Classes Of Brill–Noether Loci And A Determinantal Formula".
*International Mathematics Research Notices*.
DOI: 10.1093/imrn/rnab025

https://works.swarthmore.edu/fac-math-stat/260