Related papers: Flag subdivisions and $\gamma$-vectors

We quantize homogeneous vector bundles over an even complex sphere $\mathbb{S}^{2n}$ as one-sided projective modules over its quantized coordinate ring. We realize them in two different ways: as locally finite $\mathbb{C}$-homs between…

After fixing a non-degenerate bilinear form on a vector space V we define an involution of the manifold of flags F in V by taking a flag to its orthogonal complement. When V is of dimension 3 we check that the Crepant Resolution Conjecture…

We consider a connected negative definite plumbing graph, and we assume that the associated plumbed 3-manifold is a rational homology sphere. We provide two new combinatorial formulae for the Seiberg-Witten invariant of this manifold. The…

In this note we complete a study of globally homogeneous Riemannian quotients $\Gamma\backslash (M,ds^2)$ in positive curvature. Specifically, $M$ is a homogeneous space $G/H$ that admits a $G$-invariant Riemannian metric of strictly…

Let G be a semisimple complex Lie group. In this article, we study Geometric Invariant Theory on a flag variety G/B with respect to the action of a principal 3-dimensional simple subgroup S of G. We determine explicitly the GIT-equivalence…

This article studies germs of holomorphic vector fields at the origin of C3 that are tangent to holomorphic foliations of codimension one. Two situations are considered. First, we assume hypotheses on the reduction of singularities of the…

We show P\'eter Csorba's conjecture that the graph homomorphism complex Hom(C_5,K_{n+2}) is homeomorphic to a Stiefel manifold, the space of unit tangent vectors to the n-dimensional sphere. For this a general tool is developed that allows…

An enumerative theory of triangulations of simplicial complexes has been developed by Stanley. A key role in his theory is played by the local $h$-polynomial of a triangulation of a simplex. This paper develops a parallel theory, in which…

The local $h$-polynomial was introduced by Stanley as a fundamental enumerative invariant of a triangulation $\Delta$ of a simplex. This polynomial is known to have nonnegative and symmetric coefficients and is conjectured to be…

We investigate the algebra of vector fields on the sphere. First, we find that linear deformations of this algebra are obstructed under reasonable conditions. In particular, we show that $hs[\lambda]$, the one-parameter deformation of the…

The equivariant $K$-theory of the semi-infinite flag manifold, as developed recently by Kato, Naito, and Sagaki, carries commuting actions of the nil-double affine Hecke algebra (nil-DAHA) and a $q$-Heisenberg algebra. The action of the…

A subvariety of a complex projective space has a well-known dual variety, which is the set of its tangent hyperplanes. The purpose of this paper is to generalise this notion for a subvariety of a quite general partial flag variety. A…

We solve the equivalence problem for rank 3 completely nonholonomic vector distributions with 6-dimensional square on a smooth manifold of arbitrary dimension n under very mild genericity conditions. The main idea is to consider the…

A conjecture of Sokal (2001) regarding the domain of non-vanishing for independence polynomials of graphs, states that given any natural number $\Delta \ge 3$, there exists a neighborhood in $\mathbb C$ of the interval $[0,…

In 2022 Kim showed when a graph $G$ is ternary (without induced cycles of length divisible by three), its independence complex $\text{Ind}(G)$ is either contractible or homotopy equivalent to a sphere. In this paper, we show that when…

We define an invariant of rational homology 3-spheres via vector fields. The construction of our invariant is a generalization of both that of the Kontsevich-Kuperberg-Thurston invariant and that of Watanabe's Morse homotopy invariant,…

We prove the following version of the Campana's orbifold conjecture: Let $X$ be a complex non-singular projective variety of dimension $n$. Let $D_1,\ldots,D_{n+1}$ be $\mathbb Z$-linearly independent effective divisors in ${\rm Div}(X)$…

Let $\nu$ be a vector measure defined on a $\sigma$-algebra $\Sigma$ and taking values in a Banach space. We prove that if $\nu$ is homogeneous and $L_1(\nu)$ is non-separable, then there is a vector measure $\tilde{\nu}:\Sigma \to…

We define an integer valued invariant of homology spheres using the methods of SU(3) gauge theory and study its behavior under orientation reversal and connected sum.

The post-Newtonian parameter $\gamma$ resulting from a universal scalar/matter coupling is investigated in Brans-Dicke-like Scalar-Tensor theories where the scalar potential is assumed to be negligible. Conversely to previous studies, we…