Related papers: Embeddings of weighted projective spaces

We establish simultaneous approximation properties of weighted first-order Sobolev orthogonal projectors onto spaces of polynomials of bounded total degree in the Euclidean unit ball. The simultaneity is in the sense that we provide bounds…

To understand the structure of an algebraic variety we often embed it in various projective spaces. This develops the notion of projective geometry which has been an invaluable tool in algebraic geometry. We develop a perfectoid analog of…

We study the continuity and compactness of embeddings for radial Besov and Triebel-Lizorkin spaces with weights in the Muckenhoupt class $A_\infty$. The main tool is a discretization in terms of an almost orthogonal wavelet expansion…

Let $X$ be a smooth complex projective variety. A recent conjecture of S. Kov\'acs states that if t\ he $p^{\text{th}}$-exterior power of the tangent bundle $T_X$ contains the $p^{\text{th}}$-exterior power of an ample vector bundle, then…

Over an algebraically closed field, the $\textit{double point interpolation}$ problem asks for the vector space dimension of the projective hypersurfaces of degree $d$ singular at a given set of points. After being open for 90 years, a…

We investigate the projective normality of smooth, linearly normal surfaces of degree 9. All non projectively normal surfaces which are not scrolls over a curve are classified. Results on the projective normality of surface scrolls are also…

In this paper we discuss the structure of weighted weak Lebesgue spaces and weighted weak Orlicz spaces on $\mathbb{R}^n$. First, we present sufficient and necessary conditions for inclusion relation between weighted weak Lebesgue spaces.…

In this note we extend the concept height on projective spaces to that of weighted height on weighted projective spaces and show how such a height can be computed. We prove some of the basic properties of the weighted height and show how it…

We generalize methods to compute various kinds of rank to the case of a toric variety $X$ embedded into projective space using a very ample line bundle $\mathcal{L}$. We find an upper bound on the cactus rank. We use this to compute rank,…

Let $\Omega $ be an open subset of $\mathbb{R}^{N}$, and let $p,\, q:\Omega \rightarrow \left[ 1,\infty \right] $ be measurable functions. We give a necessary and sufficient condition for the embedding of the variable exponent space…

Let $X$ be a $d$ dimensional projective manifold, $E$ be an ample vector bundle on $X$ and $0\le \lambda_N\le \lambda_{N-1} \le \cdots \le \lambda_1 \le \operatorname{rank}(E)$ be a partition of $d-2$. We prove that the Schur class…

We study the projective normality of the projective bundle of an Ulrich vector bundle embedded through the complete linear system of its tautological line bundle. The focus will be on Ulrich bundles defined over curves, surfaces with…

Let $(X,L)$ be an $n$-dimensional polarized variety. Fujita's conjecture says that if $L^n>1$ then the adjoint bundle $K_X+nL$ is spanned and $K_X+(n+1)L$ is very ample. There are some examples such that $K_X+nL$ is not spanned or…

The embedding constants of the Sobolev spaces $\mathring{W}^n_2[0;1] \hookrightarrow \mathring{W}^k_\infty[0; 1]$ ($0\leqslant k \leqslant n-1$) are studied. A relation of the embedding constants with the norms of the functionals $f\mapsto…

Let $P_{\lambda\Sigma_n}$ be the Ehrhart polynomial associated to an intergal multiple $\lambda$ of the standard symplex $\Sigma_n \subset \mathbb{R}^n$. In this paper we prove that if $(M, L)$ is an $n$-dimensional polarized toric manifold…

A more general notion of weight called admissible is introduced and then an investigation is carried out on the a.e. convergence of weighted strong laws of large numbers and their applications to weighted one-sided ergodic Hilbert…

Let $X$ be a complex smooth projective variety of dimension $d$. Under some assumption on the cohomology of $X$, we construct mutually orthogonal idempotents in $CH_d(X \times X) \otimes \Q$ whose action on algebraically trivial cycles…

We study random exponential sums of the form $\sum_{k=1}^nX_k\times\ex p\{i(\lambda_k^{(1)}t_1+...+\lambda_k^{(s)}t_s)\}$, where $\{X_n\}$ is a sequence of random variables and $\{\lambda_n^{(i)}:1\leq i\leq s\}$ are sequences of real…

In this paper we prove that if the r-th tensor power of the tangent bundle of a smooth projective variety X contains the determinant of an ample vector bundle of rank at least r, then X is isomorphic either to a projective space or to a…

For $k \in \mathbb{Z}_{>0}$, let $\mathcal{H}^{(k)}_{g,n}$ denote the vector bundle over $\mathfrak{M}_{g,n}$ whose every fiber consists of meromorphic $k$-differentials with poles of order at most $k-1$ on a fixed Riemman surface of genus…