Related papers: On the restriction formula

In this article, we obtain two sharp equality conditions in the restriction formula on complex singularity exponents: an equality between the codimension of the zero variety of related multiplier ideal sheaves and the relative codimension…

In the present article, we establish an equality condition in the restriction formula on jumping numbers by giving a sharp lower bound of the dimension of the support of a related coherent sheaf. As applications, we obtain equality…

The goal of this note is to present some recent results of our research concerning multiplier ideal sheaves on complex spaces and singularities of plurisubharmonic functions. We firstly introduce multiplier ideal sheaves on complex spaces…

Let $\phi$ be a psh function on a bounded pseudoconvex open set $\Omega \subset \C^n$, and let ${\cal I}(\phi)$ be the associated multiplier ideal sheaf. Motivated by resolution of singularities issues, we establish an effective version of…

In this note, we show how to apply the original $L^2$-extension theorem of Ohsawa and Takegoshi to the standard basis of a multiplier ideal sheaf associated with a plurisubharmonic function. In this way, we are able to reprove the strong…

The goal of this contribution is to investigate L${}^2$ extension properties for holomorphic sections of vector bundles satisfying weak semi-positivity properties. Using techniques borrowed from recent proofs of the Ohsawa-Takegoshi…

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.

Suppose that $X$ is an analytic subvariety of a Stein manifold $M$ and that $\varphi$ is a plurisubharmonic (psh) function on $X$ which is dominated by a continuous psh exhaustion function $u$ of $M$. Given any number $c>1$, we show that…

We present an algebro-geometric perspective on some generalizations, due to S. Takagi, of the restriction theorem for multiplier ideals. The first version of the restriction theorem for multiplier ideals was discovered by Esnault and…

In this article we prove a theorem of Ohsawa-Takegoshi type on compact K\"ahler manifolds. Our arguments follow the "standard" approach for this kind of extension results; however, there are many complications arising from the…

The main goal of this paper is to construct an algebraic analogue of quasi-plurisubharmonic function (qpsh for short) from complex analysis and geometry. We define a notion of qpsh function on a valuation space associated to a quite general…

In a previous work we proved a spectral multiplier theorem of Mihlin--H\"ormander type for two-dimensional Grushin operators $-\partial_x^2 - V(x) \partial_y^2$, where $V$ is a doubling single-well potential, yielding the surprising result…

Consider a second order, strongly elliptic negative semidefinite differential operator $L$ (maybe a system) on a compact Riemannian manifold $\overline{M}$ with smooth boundary, where the domain of $L$ is defined by a coercive boundary…

The goal of this survey is to describe some recent results concerning the L 2 extension of holomorphic sections or cohomology classes with values in vector bundles satisfying weak semi-positivity properties. The results presented here are…

In this expository article we first give an overview on multiplier ideal sheaves and geometric problems in K\"ahlerian and Sasakian geometries. Then we review our recent results on the relationship between the support of the subschemes cut…

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.

In $L^2$ extension theorems from a singular hypersurface in a complex manifold, important roles are played by certain measures such as the Ohsawa measure which determine when a given function can be extended. We show that the singularity of…

Given an effective Q-divisor D on a smooth complex variety, one can associate to D its multiplier ideal sheaf J(D), which measures in a somewhat subtle way the singularities of D. Because of their strong vanishing properties, these ideals…

Let G be a real semi-simple Lie group and H a closed subgroup which admits an open orbit on the flag manifold of a minimal parabolic subgroup. Let V be a Harish-Chandra module. A sharp finite bound is given for the dimension of the space of…

We prove that a totally real manifold (of maximal dimension) is a boundary uniqueness set for a psh function on an almost complex manifold.