相关论文: Counter-examples to a conjecture of Karpenko for s…

Let $G$ be a split semisimple linear algebraic group and let $X$ denote the generically twisted variety of Borel subgroups in $G$. Nikita Karpenko conjectured that the map from the Chow ring of $X$ to the associated graded ring of the…

Let $G$ be a compact Lie group and $T$ its maximal torus. In this paper, we try to compute $gr_{\gamma}^*(G/T)$ the graded ring associated with the gamma filtration of the complex $K$-theory $K^0(G/T)$ for $G=Spin(n)$. In particular, we…

In this paper, we generalize a result of Karpenko on the torsion in the second quotient of the gamma filtration for Severi-Brauer varieties to higher degrees. As an application, we provide a nontrivial torsion in higher Chow groups and the…

Let $X$ be a connected component of the maximal orthogonal grassmannian of a generic $n$-dimensional quadratic form $q$ with trivial Clifford invariant. Consider the canonical epimorphism $\phi$ from the Chow ring of $X$ to the associated…

In this paper we examine the saturation conjecture on decompositions of tensor products of irreducible representations for complex semisimple algebraic groups of type $D$ (the even \emph{spin} groups: Spin$(2n)$ for $n\ge 4$ an integer),…

We construct a weak version of the homological first Steenrod square, a natural transformation from the modulo two Chow group to the Chow group modulo two and two-torsion. No assumption is made on the characteristic of the base field. As an…

Let $G$ be a complex reductive algebraic group, $T$ a maximal torus in $G$, $B$ a Borel subgroup of $G$ containing $T$, $W$ the Weyl group of $G$ with respect to $T$. Let $w$ be an element of $W$. Denote by $X_w$ the Schubert subvariety of…

We classify when the blowup of a complex Grassmannian $G(k, n)$ along a smooth Schubert subvariety $Z$ is Fano. We compute almost all the two-point, genus zero Gromov-Witten invariants of the blowup when $Z=G(k, n-1)$. We further prove a…

Let X be a Gorenstein orbifold and let Y be a crepant resolution of X. We state a conjecture relating the genus-zero Gromov--Witten invariants of X to those of Y, which differs in general from the Crepant Resolution Conjectures of Ruan and…

We prove a recent conjecture of the fourth named author with P. Norbury that states a system of universal polynomial relations among the kappa classes on the moduli spaces of algebraic curves. The proof involves localization and…

A minimal presentation of the cohomology ring of the flag manifold $GL_n/B$ was given in [A. Borel, 1953]. This presentation was extended by [E. Akyildiz-A. Lascoux-P. Pragacz, 1992] to a non-minimal one for all Schubert varieties. Work of…

We describe the equivariant Chow ring of the wonderful compactification $X$ of a symmetric space of minimal rank, via restriction to the associated toric variety $Y$. Also, we show that the restrictions to $Y$ of the tangent bundle $T_X$…

We prove that if $X \to Y$ is a (geometrically) regular morphism of Noetherian schemes, then from a Nisnevich-local perspective, the Gersten complex for Quillen $K$-theory on $X$ becomes acyclic in degrees beyond the Krull dimension of $Y$.…

Let G be a compact connected Lie group and p : E \to {\Sigma}^2V a principal G-bundle with a characteristic map \alpha : A={\Sigma}V \to G. By combining cone decomposition arguments in Iwase-Mimura-Nishimoto [3,5] with computations of…

For generic time-reversal invariant systems with spin-orbit couplings, we clarify a close relationship between the Z$_2$ topological order and the spin Chern number proposed by Kane and Mele and by Sheng {\it et al.}, respectively, in the…

Let $F$ be a field. Following the resolution of Milnor's conjecture relating the graded Witt ring of $F$ to its mod-2 Milnor $K$-theory, a major problem in the theory of symmetric bilinear forms is to understand, for any positive integer…

To a pair $(A,s)$ consisting of a smooth, cyclic $A_\infty$-algebra $A$ and a splitting $s$ of the Hodge filtration on its Hochschild homology Costello (2005) associates an invariant which conjecturally generalizes the total descendant…

In this paper, we compute categorical entropy of spherical twists. In particular, we prove that Gromov-Yomdin type conjecture holds for spherical twists. Moreover, we construct counterexamples of Gromov-Yomdin type conjecture for K3…

We prove that the Schubert structure constants of the quantum $K$-theory ring of any minuscule flag variety or quadric hypersurface have signs that alternate with codimension. We also prove that the powers of the deformation parameter $q$…

We establish certain "non-triviality" results for several filtrations of the smooth and topological knot concordance groups. First, as regards the n-solvable filtration of the topological knot concordance group defined by K. Orr, P.…