相关论文: A GIT proof of W{\l}odarczyk's weighted factorizat…

In the present paper we prove Besocovich weighted ergodic theorem for positive contractions acting on Orlich-Kantorovich space. Our main tool is the use of methods of measurable bundles of Banach-Kantorovich lattices.

We prove the Lukacs characterization of the Wishart distribution on non-octonion symmetric cones of rank greater than 2. We weaken the smoothness assumptions in the version of the Lukacs theorem of [Bobecka-Weso{\l}owski, Studia Math. 152…

For a normal projective variety $X$, the $\bf Q$-factoriality defect $\sigma(X)$ is defined to be the rank of the quotient of the group of Weil divisors by the subgroup of Cartier ones. We prove a slight improvement of a topological formula…

We give evidence for a uniformization-type conjecture, that any algebraic variety can be altered into a variety endowed with a tower of smooth fibrations of relative dimension one.

Ore proved that a finite group is cyclic if and only if its subgroup lattice is distributive. Now, since every subgroup of a cyclic group is normal, we call a subfactor planar algebra cyclic if all its biprojections are normal and form a…

Polytopes are ubiquitous in different areas of mathematics. Gleason and Hubard established a factorisation theorem, stating that every abstract polytope has a unique factorisation into prime polytopes. We compute the automorphism group of a…

Using results of Hironaka-Matsumura and Faltings, we prove a strong version of the well known Fulton-Hansen connectivity theorem for weighted projective spaces. As a consequence we get the following result. If $Y$ is an irreducible…

We show that stack-theoretic resolution of singularities preserving normal crossings (partial desingularization) by weighted blowings-up, can be obtained in a simple direct way from a splitting theorem of the first and third authors, using…

Let $G$ be a simple algebraic group of adjoint type over the field $\mathbb{C}$ of complex numbers. Let $B$ be a Borel subgroup of $G$ containing a maximal torus $T$ of $G$. Let $w$ be an element of the Weyl group $W$ and let $X(w)$ be the…

Testable weighted graph parameters and equivalent notions of testability are investigated based on papers of Laszlo Lovasz and coauthors. We prove that certain balanced minimum multiway cut densities are testable. Using this fact, quadratic…

We prove a cohomological splitting result for Hamiltonian fibrations over enumeratively rationally connected symplectic manifolds As a key application, we prove that the cohomology of a smooth, projective family over a smooth (stably)…

The purpose of this paper is to prove the following theorem. Let $X$ be a projective normal variety defined over an algebraically closed field of characteristic zero and let $\Omega_{X}^{1}\to L$ be a one-dimensional foliation on $X$. If…

We develop a ring-theoretic approach for blowing up many noncommutative projective surfaces. Let T be an elliptic algebra (meaning that, for some central element g of degree 1, T/gT is a twisted homogeneous coordinate ring of an elliptic…

We show that the Grauert blow-down of a holomorphic negative line bundle $L$ over a compact complex space is a quadratic transform if and only if $k_0L^*$ is very ample and $(k_0+1)L^*$ is globally generated, where $k_0$ is the initial…

In this paper, we provide a version of the classical result of Kowalski and S\l odkowski that generalizes the famous Gleason-Kahane-$\dot{\rm Z}$elazko (GKZ) theorem by characterizing multiplicative linear functionals amongst all…

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,…

If $G$ is a strongly connected finite directed graph, the set $\mathcal{T}G$ of rooted directed spanning trees of $G$ is naturally equipped with a structure of directed graph: there is a directed edge from any spanning tree to any other…

We give a new simple proof of boundedness of the family of semistable sheaves with fixed numerical invariants on a fixed smooth projective variety. In characteristic zero our method gives a quick proof of Bogomolov's inequality for…

Let U be a smooth quasi-projective variety over a field k that is finite, the algebraic closure of a finite field or algebraically closed of characteristic 0. Let X be a suitable projective compactification of U, and D an effective divisor…

We prove analogs of Whitehead's theorem (from algebraic topology) for both the Chow groups and for the Grothendieck group of coherent sheaves: a morphism between smooth projective varieties whose pushforward is an isomorphism on the Chow…