Related papers: P-flag spaces and incidence stratifications

For a manifold $W$ and an $E_d$-algebra $A$, the factorisation homology $\int_W A$ can be seen as a generalisation of the classical configuration space of labelled particles in $W$. It carries an action by the diffeomorphism group…

This work provides a unified formalism for studying difference and (Hasse-) differential algebraic geometry, by introducing a theory of "iterative Hasse rings and schemes". As an application, Hasse jet spaces are constructed generally,…

We introduce tangent cones of subsets of cartesian powers of a real closed field, generalising the notion of the classical tangent cones of subsets of Euclidean space. We then study the impact of non-archimedean stratifications…

The standard Poisson structures on the flag varieties G/P of a complex reductive algebraic group G are investigated. It is shown that the orbits of symplectic leaves in G/P under a fixed maximal torus of G are smooth irreducible locally…

We construct completely integrable systems on the dual of the Lie algebra of any compact Lie group $K$ with respect to the standard Lie-Poisson structure. These systems generalize key properties of Gelfand-Zeitlin systems: A) the pullback…

The paper describes the algebraic structure of the graded algebra of differentially homogeneous polynomials of fixed finite order. We show that it is a finitely generated algebra, and we exhibit a minimal set of generators. Along the way,…

Stanley's theory of $(P,\omega)$-partitions is a standard tool in combinatorics. It can be extended to allow for the presence of a restriction, that is a given maximal value for partitions at each vertex of the poset, as was shown by Assaf…

Let G be a classical complex Lie group, P any parabolic subgroup of G, and X = G/P the corresponding homogeneous space, which parametrizes (isotropic) partial flags of subspaces of a fixed vector space. In the mid 1990s, Fulton, Pragacz,…

For curved projective manifolds we introduce a notion of a normal tractor frame field, based around any point. This leads to canonical systems of (redundant) coordinates that generalise the usual homogeneous coordinates on projective space.…

Let $\mathbf{G}$ be one of the ind-groups $GL(\infty)$, $O(\infty)$, $Sp(\infty)$ and $\mathbf{P}\subset \mathbf{G}$ be a splitting parabolic ind-subgroup. The ind-variety $\mathbf{G}/\mathbf{P}$ has been identified with an ind-variety of…

In this work we study the moduli spaces of instanton bundles on the flag twistor space $F:=F(0,1,2)$. We stratify them in terms of the minimal twist supporting global sections and we introduce the notion of (special) 't Hooft bundle on $F$.…

Let $\cP=G/P$ be a homogeneous projective variety with $G$ a reductive group and $P$ a parabolic subgroup. In positive characteristic we exhibit for $G$ of low rank a Karoubian complete strongly exceptional poset of locally free sheaves…

We give the formula for multiplying a Schubert class on an odd orthogonal or symplectic flag manifold by a special Schubert class pulled back from a Grassmannian of maximal isotropic subspaces. This is also the formula for multiplying a…

Let $P$ be a finite poset. We will show that for any reasonable $P$-persistent object $X$ in the category of finite topological spaces, there is a $P-$ weighted graph, whose clique complex has the same $P$-persistent homology as $X$.

In this paper, given a semisimple algebraic group $\bf G$ of rank 2, we construct a special semiorthogonal decomposition in the derived category of coherent sheaves on the flag variety ${\bf G}/{\bf B}$. These decompositions are defined…

The space of unitary local systems of rank one on the complement of an arbitrary divisor in a complex projective algebraic variety can be described in terms of parabolic line bundles. We show that multiplier ideals provide natural…

In this follow-up to [16], we continue developing the notion of a lego category and its many applications to stratifiable spaces and the computation of their Grothendieck classes. We illustrate the effectiveness of this construction by…

The classification of flag-transitive generalised quadrangles is a long-standing open problem at the interface of finite geometry and permutation group theory. Given that all known flag-transitive generalised quadrangles are also…

We express the diagonals of projective, Grassmann and, more generally, flag bundles of type (A) using the zero schemes of some vector bundle sections, and do the same for their single point subschemes. We discuss diagonal and point…

For any finite poset $P$ we have the poset of isotone maps $\text{Hom}(P,\mathbb{N})$, also called $P^{op}$-partitions. To any poset ideal ${\mathcal J}$ in $\text{Hom}(P,\mathbb{N})$, finite or infinite, we associate monomial ideals: the…