Related papers: On the restriction formula

We show that the restriction to a smooth transversal section commutes to the computation of multiplier ideals and V-filtrations. As an application we prove the constancy of the spectrum along any stratum of a Whitney regular stratification.

For a real-valued measurable function $f$ and a nonnegative, nondecreasing function $\phi$, we first obtain a Chebyshev type inequality which provides an upper bound for $\displaystyle \phi(\lambda_{1}) \mu(\{x \in \Omega : f(x) \geq…

We give a condition on the curvature tensors of Riemannian manifolds that admit Lipschitz approximation by polyhedral metrics with curvature bounded below or above. We show that this condition is also sufficient for the existence of local…

In a setting of a complex manifold with a fixed positive line bundle and a submanifold, we consider the optimal Ohsawa-Takegoshi extension operator, sending a holomorphic section of the line bundle on the submanifold to the holomorphic…

Let (RmR), (SmS) and (TmT) be Noetherian local rings sharing the same residue eld k and prime characteristic p > 0. We establish some formulas relating the h-function and s-multiplicity of the ber product R T S in terms of the h-functions…

We shall give conditions on the illuminations $\varphi_{i}$ such that the solutions to Maxwell's equations \[ \left\{ \begin{array}{l} {\rm curl} E^{i}=i\omega\mu H^{i}\qquad\text{in }\Omega,\\ {\rm curl}…

We establish a rather unexpected and simple criterion for the boundedness of Schur multipliers $S_M$ on Schatten $p$-classes which solves a conjecture proposed by Mikael de la Salle. Given $1 < p < \infty$, a simple form our main result…

Suppose that $X$ is a projective variety over an algebraically closed field of characteristic $p > 0$. Further suppose that $L$ is an ample (or more generally in some sense positive) divisor. We study a natural linear system in $|K_X + L|$.…

We first show that the projection image of a discrete definable set is again discrete for an arbitrary definably complete locally o-minimal structure. This fact together with the results in a previous paper implies tame dimension theory and…

We develop a special multilinear complex interpolation theorem that allows us to prove an optimal version of the bilinear H\"ormander multiplier theorem concerning symbols that lie in the Sobolev space $L^r_s(\mathbb R^{2n})$, $2\le…

We prove that certain roots of the Bernstein-Sato polynomial (i.e. b-function) are jumping coefficients up to a sign, showing a partial converse of a theorem of L. Ein, R. Lazarsfeld, K.E. Smith, and D. Varolin. We also prove that certain…

We consider generalized Orlicz-Morrey spaces $M_{\Phi,\varphi}(\Rn)$ including their weak versions $WM_{\Phi,\varphi}(\Rn)$. In these spaces we prove the boundedness of the Riesz potential from $M_{\Phi,\varphi_1}(\Rn)$ to…

In this expository introductory text we discuss the multiplier ideals in algebraic geometry. We state Kawamata-Viehweg's and Nadel's vanishing theorems, give a proof (following Ein and Lazarsfeld) of Koll\'ar's bound on the maximal…

In this paper, we provide sufficient conditions for the functions $\psi$ and $\phi$ to be the approximate duals in the Hardy space $H^p(\mathbb{R})$ for all $0<p\leq1$. Based on these conditions, we obtain the wavelet series expansion in…

We prove an extension theorem for effective plt pairs $(X,S+B)$ of non-negative Kodaira dimension $\kappa (K_X+S+B)\geq 0$. The main new ingredient is a refinement of the Ohsawa-Takegoshi $L^2$ extension theorem involving singular hermitian…

Let $\varphi$ be a function in the complex Sobolev space $W^*(U)$, where $U$ is an open subset in $\mathbb{C}^k$. We show that the complement of the set of Lebesgue points of $\varphi$ is pluripolar. The key ingredient in our approach is to…

We establish a lower bound for the complexity of multiplying two skew polynomials. The lower bound coincides with the upper bound conjectured by Caruso and Borgne in 2017, up to a log factor. We present algorithms for three special cases,…

Let $A$ be an excellent two-dimensional normal local ring containing an algebraically closed field and let $X\to \mathrm{Spec} (A)$ be a resolution of singularity. We prove a theorem giving a condition under which the dimension of the…

In this paper we consider Fourier multiplier operators between vector-valued Besov spaces with different integrability exponents $p$ and $q$, which depend on the type $p$ and cotype $q$ of the underlying Banach spaces. In a previous paper…

Let (X,L) be a polarized compact manifold, i.e. L is an ample line bundle over X and denote by H the infinite dimensional space of all positively curved Hermitian metrics on L equipped with the Mabuchi metric. In this short note we show,…