Related papers: Standard Monomials for Positroid Varieties

We give a crystal-theoretic proof that nonsymmetric Macdonald polynomials specialized to $t=0$ are affine Demazure characters. We explicitly construct an affine Demazure crystal on semistandard key tabloids such that removing the affine…

In this paper we determine the facets of the polyhedral cone generated by the exponent set of the monomials defining the base ring associated to some transversal polymatroid. We need the description of these facets to find the canonical…

There is a natural descending filtration on the singular cohomology of a complex smooth projective variety called the coniveau filtration. The generalized Hodge conjecture would imply, rather trivially, that the coniveau filtration is…

We construct canonical Hasse invariants for arbitrary Shimura varieties of Hodge type for the mu-ordinary locus.

Let $(M, q)$ be a quadratic projective module of an odd rank over an commutative ring, where the form $q$ is semiregular, with global Witt index of at least $2$, and with $\mathrm{rk}(M) \ge 7$. We prove standard commutator formulae and…

We calculate the Borel-Moore homology of affine Springer fibers of type $A$ associated to some regular semisimple nil elliptic elements. As a result, we obtain bigraded $\mf{S}_{n}$-modules whose bigraded Frobenius series are generalization…

We show that the Poincar\'e lemma we proved elsewhere in the context of crystalline cohomology of higher level behaves well with regard to the Hodge filtration. This allows us to prove the Poincar\'e lemma for transversal crystals of level…

For any two degrees coprime to the rank, we construct a family of ring isomorphisms parameterized by GSp(2g) between the cohomology of the moduli spaces of stable Higgs bundles which preserve the perverse filtrations. As consequences, we…

We give a new construction of the Bott-Samelson variety $Z$ as the closure of a $B$-orbit in a product of flag varieties $(G/B)^l$. This also gives an embedding of the projective coordinate ring of the variety into the function ring of a…

The aim of this article is to investigate central-valued identities involving pairs of endomorphisms on prime rings equipped with an involution of the second kind. Extending the recent contributions of Mir et al. (2020) and Boua et al.…

We study certain complexes of differential forms, including reverse de Rham complexes, on (real or complex) Poisson manifolds, especially holomorphic log-symplectic ones. We relate these to the degeneracy divisor and rank loci of the…

We combine classic stability results for foliations with recent results on deformations of Lie groupoids and Lie algebroids to provide a cohomological characterization for rigidity of compact foliations on compact manifolds.

Let ${\cal L}$ be a variation of Hodge structures on the complement $X^{*}$ of a normal crossing divisor (NCD) $ Y$ in a smooth analytic variety $X$ and let $ j: X^{*} = X - Y \to X $ denotes the open embedding. The purpose of this paper is…

We classify valuations on lattice polygons with values in the ring of formal power series that commute with the action of the affine unimodular group. A typical example of such valuations is induced by the Laplace transform, but as it turns…

The paper proposes an algorithm which could identify a general class of pdes describing dynamical systems with similar symmetries. The way that will be followed starts from a given group of symmetries, the determination of the invariants…

We propose a general study of standard bases of polynomial ideals with parameters in the case where the monomial order is arbitrary. We give an application to the computation of the stratification by the local Hilbert-Samuel function.…

This is my habilitation thesis. As the tradition wants, I tried to give an introduction of my field of research. I post it on the ArXiv with the hope it can be useful to young researchers looking for a short and friendly text on…

We introduce deformations of the space of (multi-diagonal) harmonic polynomials for any finite complex reflection group of the form W=G(m,p,n), and give supporting evidence that this space seems to always be isomorphic, as a graded…

Jun-Muk Hwang and Ngaiming Mok have proved the rigidity of irreducible Hermitian symmetric spaces of compact type under Kaehler degeneration. I adapt their argument to the algebraic setting in positive characteristic, where cominuscule…

Recent results of Kahle and Miller give a method of constructing primary decompositions of binomial ideals by first constructing "mesoprimary decompositions" determined by their underlying monoid congruences. These mesoprimary…