Related papers: Joint spectrum shrinking maps on projections

We study automorphisms of the Hilbert scheme of $n$ points on a generic projective K3 surface $S$, for any $n \geq 2$. We show that the automorphism group of $S^{[n]}$ is either trivial or generated by a non-symplectic involution and we…

We give a description of a weakly continuous rank preserving map on a reflexive algebra on complex Hilbert space with commutative completely distributive subspace lattice. We show that the implementation of a rank preserving map can be…

Let $S_{g}$ be a general prime K3 surface in $P^g$ of genus $g \geq 3$ or a general double cover of $P^2$ ramified along a sextic curve for $g = 2$ and $S = S_{i,g}$ its {\it i}-th Veronese embedding. In this article we compute the corank…

Let ${\mathcal M}_2(\mathbb F)$ be the algebra of 2$\times$2 matrices over the real or complex field $\mathbb F$. For a given positive integer $k\geq 1$, the $k$-commutator of $A$ and $B$ is defined by $[A,B]_k=[[A,B]_{k-1},B]$ with…

For a Reproducing Kernel Hilbert Space on a complex domain we give a formula that describes the Hermitean metrics on the domain which are pull-backs of some metric on the (dual of) the RKHS via the evaluation map. Then we consider the…

This article shows that every non-isotropic harmonic 2-torus in complex projective space factors through a generalised Jacobi variety related to the spectral curve. Each map is composed of a homomorphism into the variety and a rational map…

Given a compact complex manifold $M$, we investigate the holomorphic vector bundles $E$ on $M$ such that $\varphi^* E$ is trivial for some surjective holomorphic map $\varphi$, to $M$, from some compact complex manifold. We prove that these…

We apply a definition of generalised super Calabi-Yau variety (SCY) to supermanifolds of complex dimension one. One of our results is that there are two SCY's having reduced manifold equal to $\mathbb{P}^1$, namely the projective super…

Given a singular connection $D$ on a vector bundle $E$ over an irreducible smooth projective curve $X$, defined over an algebraically closed field, we show that there is a unique maximal subsheaf of $E$ on which $D$ induces a nonsingular…

We prove the existence and uniqueness of harmonic maps in degree one homotopy classes of closed, orientable surfaces of positive genus, when the target has conic points with cone angles less than $2\pi$. For a cone point $p$ of cone angle…

Let R be a compact, connected, orientable surface of genus g with p boundary components. Let C(R) be the complex of curves on R and Mod_R^* be the extended mapping class group of R. Suppose that either g = 2 and p > 1 or g > 2 and p >= 0.…

On unitary compact groups the decomposition of a generic element into product of reflections induces a decomposition of the characteristic polynomial into a product of factors. When the group is equipped with the Haar probability measure,…

Each infinitesimally faithful representation of a reductive complex connected algebraic group $G$ induces a dominant morphism $\Phi$ from the group to its Lie algebra $\g$ by orthogonal projection in the endomorphism ring of the…

A reflection mapping is a singular holomorphic mapping obtained by restricting the quotient mapping of a complex reflection group. We study the analytic structure of double point spaces of reflection mappings. In the case where the image is…

Let $G$ be a locally compact abelian topological group. For locally bounded measurable functions $\varphi: G\to\Bbb {C}$ we discuss notions of spectra for $\varphi$ relative to subalgebras of $L^{1}(G)$. In particular we study polynomials…

Let $\{S_i\}_{i=1}^{l}$ be an iterated function system(IFS) on $\mathbb{R}^d$ with attractor K. Let $\pi$ be the canonical projection. In this paper we define a new concept called "projection pressure" $P_\pi(\phi)$ for $\phi\in…

Given an idempotent operator $E$ in a complex Hilbert space ${\mathcal H}$, one can associate to it two orthogonal projections: - The polar decomposition $2E-1=(2P-1)|2E-1|$ provides an orthogonal projection $P$. That the unitary part in…

Let $X$ be a smooth surface and let $\varphi:X\to\mathbb{P}^N$, with $N\geq 4$, be a finitely ramified map which is birational onto its image $Y = \varphi(X)$, with $Y$ non-degenerate in $\mathbb{P}^N$. In this paper, we produce a lower…

The purpose of this article is to prove a generalisation of the Besicovitch-Federer projection theorem about a characterisation of rectifiable and unrectifiable sets in terms of their projections. For an $m$-unrectifiable set…

We start with considering rank one self-adjoint perturbations $A_\alpha = A+\alpha(\,\cdot\,,\varphi)\varphi$ with cyclic vector $\varphi\in \mathcal{H}$ on a separable Hilbert space $\mathcal H$. The spectral representation of the…