Related papers: The exactness of a general Skoda complex

Let $\mathfrak{a}$ be a proper ideal of a commutative noetherian ring $R$ and $d$ a positive integer. We answer Hartshorne's question on cofinite complexes completely in the cases $\mathrm{dim}R=d$ or $\mathrm{dim}R/\mathfrak{a}=d-1$ or…

We consider symmetric (under the action of products of finite symmetric groups) real algebraic varieties and semi-algebraic sets, as well as symmetric complex varieties in affine and projective spaces, defined by polynomials of degrees…

Let $\Omega$ denote an algebra of sets and $\mu$ a $\sigma$-finite measure. We then prove that the completion of $\Omega$ under the pseudometric $d(A,B)$ = $\mu^{\ast}(A \triangle B)$ is $\sigma$-algebra isomorphic and isometric to the…

The initial motivation for this paper is to discuss a more concrete approach to an approximation theorem of Axler and Shields, which says that the uniform algebra on the closed unit disc closure(D) generated by z and h --- where h is a…

Polynomial completeness results aim at characterizing those functions that are induced by polynomials. Each polynomial function is congruence preserving, but the opposite need not be true. A finite algebraic structure $\mathbf{A}$ is called…

We prove a compactness theorem for full Boolean-valued models. As an application, we show that if $T$ is a complete countable theory and $\mathcal{B}$ is a complete Boolean algebra, then $\lambda^+$-saturated $\mathcal{B}$-valued models of…

We note that the vanishing and injectivity theorems of Koll\'ar and Esnault-Viehweg can be used to give a quick algebraic proof of a strengthening of the Ein-Lazarsfeld Skoda-type division theorem for global sections of adjoint line bundles…

We show that if there exists a countable Borel equivalence relation which is hyper-hyperfinite but not hyperfinite then the complexity of hyperfinite countable Borel equivalence relations is as high as possible, namely,…

We define a weighted multiplicity function for closed geodesics of given length on a finite area Riemann surface. These weighted multiplicities appear naturally in the Selberg trace formula, and in particular their mean square plays an…

We give an explicit formula for the degree of the Grothendieck polynomial of a Grassmannian permutation and a closely related formula for the Castelnuovo-Mumford regularity of the Schubert determinantal ideal of a Grassmannian permutation.…

In this note, for the multiplier ideal sheaves with weights $\log\sum_{i}|z_{i}|^{a_{i}}$, we present the sufficient and necessary condition of the existence of decreasing equisingular approximations with analytic singularities.

Demailly, Ein and Lazarsfeld \cite{DEL} proved the subadditivity theorem for multiplier ideals, which states the multiplier ideal of the product of ideals is contained in the product of the individual multiplier ideals, on non-singular…

In the present article, we obtain an optimal support function of weighted $L^2$ integrations on superlevel sets of psh weights, which implies the strong openness property of multiplier ideal sheaves.

We show that all integrally closed ideals on log terminal surfaces are multiplier ideals by extending an existing proof for smooth surfaces.

Let X be a smooth variety and J, K two ideal sheaves on X. We prove the following formula relating the multiplier ideals of J, K and J+K: I(X, c(J+K))\subset \sum_{a+b=c} I(X, aJ)\cdot I(X,bK). An analogous formula holds for the asymptotic…

A theorem is proved concerning approximation of analytic functions by multivariate polynomials in the $s$-dimensional hypercube. The geometric convergence rate is determined not by the usual notion of degree of a multivariate polynomial,…

Using recent results of Berman and Boucksom we show that for a non-pluripolar compact set K in C^d and an admissible weight function w=e^{-\phi} any sequence of so-called optimal measures converges weak-* to the equilibrium measure…

We prove that, for an arbitrary topological space $X$, the following two conditions are equivalent: (a) Every open cover of $X$ has a finite subset with dense union (b) $X$ is $D$-pseudocompact, for every ultrafilter $D$. Locally, our…

The classical Bertini theorem on generic intersection of an algebraic set with hyperplanes states the following: \emph{Let X be a nonsingular closed subvariety of $\mathbb{P}^n_k$, where $k$ is an algebraically closed field. Then there…

Menger's conjecture that Menger spaces are /sigma-compact is false; it is true for analytic subspaces of Polish spaces and undecidable for more complex definable subspaces of Polish spaces. For non-metrizable spaces, analytic Menger spaces…