Related papers: A note on Hessenberg varieties
We study geometric and topological properties of Hessenberg varieties of codimension one in the type A flag variety. Our main results: (1) give a formula for the Poincar\'e polynomial, (2) characterize when these varieties are irreducible,…
We give a revised version of Schmidt's treatment of forms in many variables, which allows us to prove a Hasse principle under more lenient conditions on the number of variables than what had previously been thought possible with these…
We extend a result of Yun on minimal reduction types to the parahoric case. This implies a uniqueness property for 2-special representations appearing in the cohomology of certain affine Springer fibers. Using this, we settle a conjecture…
Let $P$ be the set of integer partitions and $D$ the subset of those with distinct parts. We extend a correspondence of Burge between partitions and binary words to give encodings of both $D$ and $D$ as words over a $k$-ary alphabet, for…
We suggest a twisted version of the categorical McKay correspondence and prove several results related to it.
Modifying an idea of E. Brietzke we give simple proofs for the recurrence relations of some sequences of binomial sums which have previously been obtained by other more complicated methods.
We present several results, including some remarks on the Hopf Lemma.
This article surveys recent developments on Hessenberg varieties, emphasizing some of the rich connections of their cohomology and combinatorics. In particular, we will see how hyperplane arrangements, representations of symmetric groups,…
We give a proof of a result of Bonet, Engli\v{s} and Taskinen filling in several details and correcting some flaws.
The Weil Conjectures are applied to the Hessenberg Varieties to obtain interesting information about the combinatorics of descents in the symmetric group. Combining this with elementary linear algebra leads to elegant proofs of some…
In this paper we construct an additive basis for the cohomology ring of a regular nilpotent Hessenberg variety which is obtained by extending all Poincar\'e duals of smaller regular nilpotent Hessenberg subvarieties. In particular, all of…
We prove the (LC) conjecture of Hochster and Huneke in some non-trivial cases. This has several applications. Recently, Brenner and Caminata answered a numerical evidence due to Dao and Smirnov on the shape of generalized Hilbert-Kunz…
This paper is an introduction, in a simplified setting, to Lusztig's theory of character sheaves. It develops a notion of character sheaves on reductive Lie algebras which is more general then such notion of Lusztig, and closer to Lusztig's…
We prove that the Deligne-Lusztig varieties associated to elements of the Weyl group which are of minimal length in their twisted class are affine. Our proof differs from the proof of He and Orlik-Rapoport and it is inspired by the case of…
We use $G$-stable pieces to construct some equidimensional varieties and as a consequence, obtain Lusztig's dimension estimates \cite[section 4]{L2}. This is a generalization of \cite{HL}.
The aim of this short note is twofold. First, we give a sketch of the proof of a recent result proved by the authors in the paper [Colombo, Crippa, and Spirito, Calc. Var. Partial Differential Equations 2015] concerning existence and…
Hessenberg varieties are a family of subvarieties of the flag variety, including the Springer fibers, the Peterson variety, and the entire flag variety itself. The seminal example arises from a problem in numerical analysis and consists for…
L. Weinstein's brilliant short proof of de Branges's Theorem is made even shorter by using computer algebra.
We appended an errata to the original submission. The purpose of this errata is to point out two errors in [2] and give a weakened version of those statements made.
We show a degree formula for a type of orthogonal Deligne--Lusztig varieties and their Pl\"ucker embeddings. This is an analog of work of Li on a unitary case.