Related papers: A geometric construction for invariant jet differe…

When $G$ is a complex reductive algebraic group and $G/K$ is a reductive symmetric space, the decomposition of $\C[G/K]$ as a $K$-module was obtained (in a non-constructive way) by Richardson, generalizing the celebrated result of…

Let $(X, \omega)$ be a weakly pseudoconvex K\"ahler manifold, $Y \subset X$ a closed submanifold defined by some holomorphic section of a vector bundle over $X,$ and $L$ a Hermitian line bundle satisfying certain positivity conditions. We…

Let $k$ be an algebraically closed field of characteristic zero, and let $X/k$ be a projective variety. The conjectures of Demailly--Green--Griffiths--Lang posit that every integral subvariety of $X$ is of general type if and only if $X$ is…

Let the DRO (Diffeomorphism, Reparametrization, Observer) algebra DRO(N) be the extension of $diff(N)\oplus diff(1)$ by its four inequivalent Virasoro-like cocycles. Here $diff(N)$ is the diffeomorphism algebra in $N$-dimensional spacetime…

For each positive integer $k$, the bundle of $k$-jets of functions from a smooth manifold, $X$, to a Lie group, $G$, is denoted by $J^k(X,G)$ and it is canonically endowed with a Lie groupoid structure over $X$. In this work, we utilize a…

A class of differential calculi is explored which is determined by a set of automorphisms of the underlying associative algebra. Several examples are presented. In particular, differential calculi on the quantum plane, the $h$-deformed…

We obtain an explicit parametrization of stationary discs glued to some Levi non-degenerate hypersurfaces. These discs form a family which is invariant under the action of biholomorphisms. We use this parametrization to construct a local…

In the first part of this paper, given a smooth family of Dirac-type operators on an odd-dimensional closed manifold, we construct an abelian gerbe-with-connection whose curvature is the three-form component of the Atiyah-Singer families…

This work deals with the structure of the isometry group of pseudo-Riemannian 2-step nilmanifolds. We study the action by isometries of several groups and we construct examples showing substantial differences with the Riemannain situation;…

In this article, first we give two formulae for the delta invariant of a complex curve singularity that can be embedded as a ${\mathbb Q}$-Cartier divisor in a normal surface singularity with rational homology sphere link. Next, we consider…

We construct a right-invariant differential calculus on the quantum supergroup GL$_h(1| 1)$ and obtain the $h$-deformed superalgebra of GL$_h(1| 1)$.

The algebraic degeneracy of holomorphic curves in a semi-Abelian variety omitting a divisor is proved (Lang's conjecture generalized to semi-Abelian varieties) by making use of the {\it jet-projection method} and the logarithmic Wronskian…

Jet isomorphism theorems for conformal geometry are discussed. A new proof of the jet isomorphism theorem for odd-dimensional conformal geometry is outlined, using an ambient realization of the conformal deformation complex. An infinite…

We consider a number of examples of groups together with an infinite conjugation invariant generating set, including: the free group with the generating set of all separable elements; surface groups with the generating set of all…

Given a compact Riemann surface X with an action of a finite group G, the group algebra Q[G] provides an isogenous decomposition of its Jacobian variety JX, known as the group algebra decomposition of JX. We obtain a method to concretely…

Let $M$ be a smooth surface in $\mathbb R^3$ (or a complex surface in $\mathbb C^3$) and $k\geq 2$ be an integer. At any point on $M$ and for any plane in $\mathbb R^3$, we construct a holomorphic map-germ $(\mathbb C^2,0)\to(\mathbb…

We investigate the finite-dimensional Lie groups whose points are separated by the continuous homomorphisms into groups of invertible elements of locally convex algebras with continuous inversion that satisfy an appropriate completeness…

In this paper we study holomorphic actions of the complex multiplicative group on complex manifolds around a singular (fixed) point. We prove linearization results for the germ of action and also for the whole action under some conditions…

We give a new version of a recent result of B{\'e}rczi-Kirwan, proving the Kobayashi and Green-Griffiths-Lang conjectures for generic hypersurfaces in the projective space , with a polynomial lower bound on the degree. Our strategy again…

Let $G$ be the identity component of the isometry group for an arbitrary curved two-point homogeneous space $M$. We consider algebras of $G$-invariant differential operators on bundles of unit spheres over $M$. The generators of this…