arXiv research

New approach proves K-stability of Fano varieties.

New cell structure on $O(3)/O(1)^3$ derived from injectivity radius computation.

We introduce the notion of $T$-stability for torsion-free Higgs sheaves as a natural generalization of the notion of $T$-stability for torsion-free coherent sheaves over compact complex manifolds. We prove similar properties to the classical ones for Higgs sheaves. In particular, we show that only saturated flags of to…

Using tools from Dirac geometry and through an explicit construction, we show that every Poisson homogeneous space of any Poisson Lie group admits an integration to a symplectic groupoid. Our theorem follows from a more general result which relates, for a principal bundle $M\to M/H$, integrations of a Dirac structure o…

Condition for intersection of real flag manifolds in complex flag manifold.

Study of weighted nonlinear flags in symplectic geometry.

New algorithm computes flag mean and median on flag manifolds.

Four geometries govern sequential and distribution-free inference.

The paper studies Finsler manifolds with a new curvature concept.

Minimal dimensions found for flag manifolds embeddings.

The paper proves Mabuchi solitons and constants on Fano admissible manifolds.

Paper provides criteria to detect non-admissible quandles via coloring.

The paper introduces geometric surgeries for flag structures and provides examples of uniformizable and non-uniformizable types.

Researchers prove formulas for flag area measures, extending previous work.

Extends residue theory to flags of holomorphic distributions.

Study equigeodesics on $G_2$-type flag manifolds, splitting tangent spaces.

Study finds numerical moduli in special 2-flags of length 5.

Study finds conditions for Kähler-Einstein metrics on flag manifolds.

The paper examines the geometry of specific submanifolds in flag manifolds.

The enumeration of normal surfaces is a key bottleneck in computational three-dimensional topology. The underlying procedure is the enumeration of admissible vertices of a high-dimensional polytope, where admissibility is a powerful but non-linear and non-convex constraint. The main results of this paper are significan…

A Lie-admissible algebra gives by anticommutativity a Lie algebra. In this work we study remarkable classes of Lie-admissible algebras such as Vinberg, PreLie algebras. We compute the corresponding binary quadratic operads and study their Koszul duality. Considering Lie algebras as Lie-admissible algebras we can define…

The paper classifies complex Dirac structures on flag manifolds.

In the recent years, a number of issues concerning distributions generating 1- flags (called also Goursat flags) has been analyzed. Presently similar questions are discussed as regards distributions generating multi-flags. (In fact, only so-called special multi-flags, to avoid functional moduli.) In particular and fore…

We investigate the secant dimensions and the identifiablity of flag varieties parametrizing flag of sub vector spaces of a fixed vector space. We give numerical conditions ensuring that secant varieties of flag varieties have the expected dimension, and that a general point on these secant varieties is identifiable.

The aim of this paper is to show that any stable complete Riemannian flag on a compact and connected manifold is conjugated to a flag of homogenus foliations (see Definitions). Also, we give a characterization of Riemannian flags that homogenus. This result is a step toward the classification of Riemannian flags.

Investigates admissible metrics on compact Kähler varieties and their stability.

Classifies minimal immersions from $S^2$ into specific flag manifolds.

Study spin chains and sigma models on flag manifolds, calculating spectra and geodesics.

The paper explores curvature positivity on Kähler and quasi-Kähler flag manifolds.

New examples show deletion type admissible pairs can be rigid under rational saturation.

In the first part of this paper we study geometric formality for generalized flag manifolds, including full flag manifolds of exceptional Lie groups. In the second part we deal with the problem of the classification of invariant almost complex structures on generalized flag manifolds using topological methods.

Topological obstructions to admissibility in $σ_k$-Loewner--Nirenberg problem

A nonlinear flag is a finite sequence of nested closed submanifolds. We study the geometry of Frechet manifolds of nonlinear flags, in this way generalizing the nonlinear Grassmannians. As an application we describe a class of coadjoint orbits of the group of Hamiltonian diffeomorphisms that consist of nested symplecti…

In this work we prove a Baum-Bott type residue theorem for flags of holomorphic foliations. We prove some relations between the residues of the flag and the residues of their correspondent foliations. We define the Nash residue for flags and we give a partial answer to the Baum-Bott type rationality conjecture in this …

We show that every flag variety contains a naturally defined homogeneous cominuscule subvariety. From the Dynkin diagram of the flag variety, we compute the Dynkin diagram of that subvariety.

A flag area measure on an $n$-dimensional euclidean vector space is a continuous translation-invariant valuation with values in the space of signed measures on the flag manifold consisting of a unit vector $v$ and a $(p+1)$-dimensional linear subspace containing $v$ with $0 \leq p \leq n-1$. Using local parallel sets, …

Holomorphic structures on quantum flag manifolds uniquely defined.

Flag manifolds are generalizations of projective spaces and other Grassmannians: they parametrize flags, which are nested sequences of subspaces in a given vector space. These are important objects in algebraic and differential geometry, but are also increasingly being used in data science, where many types of data are…

The paper describes invariant twisted Kähler-Einstein metrics on flag varieties.

The study classifies transverse spheres in flag manifolds and finds new examples.

If the flag curvature of a Finsler manifold reduces to sectional curvature, then locally either the Finsler metric is Riemannian, or the flag curvature is isotropic.

A flag is a sequence of nested subspaces. Flags are ubiquitous in numerical analysis, arising in finite elements, multigrid, spectral, and pseudospectral methods for numerical PDE; they arise in the form of Krylov subspaces in matrix computations, and as multiresolution analysis in wavelets constructions. They are comm…

Note refutes examples of Landsberg surfaces with vanishing flag curvature.

One of the most important problems in Finsler geometry is to classify Finsler metrics of scalar flag curvature. In this paper, we study the classification problem of Randers metrics of scalar flag curvature. Under the condition that $β$ is a Killing 1-form, we obtain some important necessary conditions for Randers metr…

Study flag curvature in homogeneous Finsler spaces with a specific metric.

The flag curvature is a natural extension of the sectional curvature in Riemannian geometry, and the S-curvature is a non-Riemannian quantity which vanishes for Riemannian metrics. There are (incomplete) non-Riemannian Finsler metrics on an open subset in R^n with negative flag curvature and constant S-curvature. In th…

Minimal equivariant embedding found for flag manifolds.

The study characterizes real flag manifolds with invariant generalized almost complex structures.