The Δ-Springer fibers Yn,λ,s, introduced by Levinson, Woo, and the second author, generalize Springer fibers for GLn(C)
Nearby in the stack
and give a geometric interpretation of the of the Delta Conjecture from algebraic combinatorics (at
t=0
). We prove that all irreducible components of the
Δ
-Springer fiber
Yn,n−1=Yn,(1n−1),n−1
are smooth. In fact, we prove that any intersection of irreducible components of
Yn,n−1
is a smooth Hessenberg variety which has the structure of an iterated Grassmannian fiber bundle. We then give a presentation of the singular cohomology ring of each irreducible component of
Yn,n−1
and a combinatorial formula for the Poincaré polynomial of an arbitrary union of intersections of irreducible components in terms of arm and leg statistics on Dyck paths.