Abstract
We introduce a family of varieties Yn,λ,s , which we call the \emph{Δ-Springer varieties}, that generalize the type A Springer fibers. We give an explicit presentation of the cohomology ring H∗(Yn,λ,s) and show that there is a symmetric group action on this ring generalizing the Springer action on the cohomology of a Springer fiber. In particular, the top cohomology groups are induction products of Specht modules with trivial modules. The λ=(1k) case of this construction gives a compact geometric realization for the expression in the Delta Conjecture at t=0. Finally, we generalize results of De Concini and Procesi on the scheme of diagonal nilpotent matrices by constructing an ind-variety Yn,λ whose cohomology ring is isomorphic to the coordinate ring of the scheme-theoretic intersection of an Eisenbud--Saltman rank variety and diagonal matrices.