Related papers: Chow-Witt rings and topology of flag varieties
We use the action of the Bockstein homomorphism on the cohomology ring $H^*(X,\mathbb{Z}_2)$ of a finite-type CW-complex $X$ in order to define the resonance varieties of $X$ in characteristic 2. Much of the theory is done in the more…
In 1998, Goresky, Kottwitz, and MacPherson showed that for certain projective varieties X equipped with an algebraic action of a complex torus T, the equivariant cohomology ring H_T(X) can be described by combinatorial data obtained from…
We study the Milnor-Witt motives which are a finite direct sum of $\mathbb{Z}(q)[p]$ and $\mathbb{Z}/\eta(q)[p]$. We show that for MW-motives of this type, we could determine an MW-motivic cohomology class in terms of a motivic cohomology…
We realise the cohomology ring of a flag manifold, more generally the coinvariant algebra of an arbitrary finite Coxeter group W, as a commutative subalgebra of a certain Nichols algebra in the Yetter-Drinfeld category over W. This gives a…
Let $G$ be a split semisimple linear algebraic group over a field and let $X$ be a generic twisted flag variety of $G$. Extending the Hilbert basis techniques to Laurent polynomials over integers we give an explicit presentation of the…
In this paper, we discuss some partitions of affine flag varieties. These partitions include as special cases the partition of affine flag variety into affine Deligne-Lusztig varieties and the affine analogue of the partition of flag…
We prove the vanishing modulo torsion of the higher direct images of the sheaf of Witt vectors (and the Witt canonical sheaf) for a purely inseparable projective alteration between normal finite quotients over a perfect field. For this, we…
We compute the \v{C}ech cohomology ring of a countable product of infinite projective spaces, and that of an infinite flag manifold. The method of our first result in fact computes the cohomology ring of a countably infinite product of…
We compute the quantum cohomology rings of the partial flag manifolds F_{n_1\cdots n_k}=U(n)/(U(n_1)\times \cdots \times U(n_k)). The inductive computation uses the idea of Givental and Kim. Also we define a notion of the vertical quantum…
The quantum cohomology algebra of the (full) flag manifold is a fundamental example in quantum cohomology theory, with connections to combinatorics, algebraic geometry, and integrable systems. Using a differential geometric approach, we…
In this article, we investigate the toric Schubert varieties in partial flag varieties $G/P$ for a connected semisimple algebraic group $G$. Using Deodhar's decomposition of Richardson varieties and the work of Pasquier, we give an explicit…
We describe a construction of Gromov-Witten invariants for flag varieties and use it to give a presentation for the quantum cohomology ring, by extending the ideas used by Bertram in the case of Grassmannians. This provides a proof for the…
We present an algorithm for computing line bundle valued cohomology classes over toric varieties. This is the basic starting point for computing massless modes in both heterotic and Type IIB/F-theory compactifications, where the manifolds…
We show that certain homological regularity properties of graded connected algebras, such as being AS-Gorenstein or AS-Cohen-Macaulay, can be tested by passing to associated graded rings. In the spirit of noncommutative algebraic geometry,…
This work investigates the vertical quantum cohomology and quantum spectra of flag bundles, uncovering new links between the Gromov-Witten theory of homogeneous fibrations and analytic number theory. Building on previous constructions by…
We use a variation of a classical construction of A. Hatcher to construct virtually all stable exotic smooth structures on compact smooth manifold bundles whose fibers have sufficiently large odd dimension (at least twice the base dimension…
Let $\mathbb{F}_{\Theta }=G/P_{\Theta }$ be a flag manifold associated to a non-compact real simple Lie group $G$ and the parabolic subgroup $% P_{\Theta }$. This is a closed subgroup of $G$ determined by a subset $% \Theta $ of simple…
Peterson varieties are subvarieties of flag varieties and their (equivariant) cohomology rings are given by Fukukawa-Harada-Masuda in type A and soon later the author with Harada and Masuda gives an explicit presentation of the…
We compute the integral cohomology ring of configuration spaces of two points on a given real projective space. Apart from an integral class, the resulting ring is a quotient of the known integral cohomology of the dihedral group of order 8…
The equivariant cohomology ring of a GKM manifold is isomorphic to the cohomology ring of its GKM graph. In this paper we explore the implications of this fact for equivariant fiber bundles for which the total space and the base space are…