  A Brill-Noether degeneracy locus is closure in $\Pic^d(C)$ of the locus of
line bundles with a specified rank function $r(a,b) = h^0(C,L(-ap-bq))$. These
loci generalize the classical Brill-Noether loci $W^r_d(C)$ as well as
Brill-Noether loci with imposed ramification. For general $(C,p,q)$ we
determine the dimension, singular locus, and intersection class of
Brill-Noether degeneracy loci, generalizing classical results about $W^r_d(C)$.
The intersection class has a combinatorial interpretation in terms of the
number of reduced words for a permutation associated to the rank function, or
alternatively the number of saturated chains in the Bruhat order. The essential
tool is a versality theorem for a certain pair of flags on $\Pic^d(C)$,
conjectured by Melody Chan and the author.
