Related papers: $L^2$-type Dolbeault isomorphisms and vanishing th…

In this paper, we first establish an $L^2$-type Dolbeault isomorphism for logarithmic differential forms by H\"{o}rmander's $L^2$-estimates. By using this isomorphism and the construction of smooth Hermitian metrics, we obtain a number of…

In this paper we establish a Nadel-type vanishing theorem on a projective manifold $X$ concerning the asymptotic multiplier ideal sheaf.

In this paper we establish a Nadel-type vanishing theorem and a Kawamata--Viehweg-type vanishing theorem concerning the asymptotic multiplier ideal sheaf on a compact K\"{a}hler manifold $X$. After that, we provide a relative variant.

In this paper, we introduce a coherent subsheaf of Saito's $S$-sheaf, which is a combination of the $S$-sheaf and the multiplier ideal sheaf. We construct its $L^2$-Dolbeault resolution, which generalizes MacPherson's conjecture on the…

In this note, we present a general version of the concavity of the minimal $L^{2}$ integrals related to multiplier ideal sheaves.

The purpose of this paper is to establish an injectivity theorem generalized to pseudo-effective line bundles with transcendental (non-algebraic) singular hermitian metrics and multiplier ideal sheaves. As an application, we obtain a Nadel…

In this paper, in order to develop a more general $L^2$-theory for the $\overline{\partial}$-operator on complex spaces, we provide $L^2$-Dolbeault fine resolutions and isomorphisms, and $L^2$-estimates, for holomorphic line bundles on…

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…

The purpose of this paper is to establish injectivity theorems for higher direct image sheaves of canonical bundles twisted by pseudo-effective line bundles and multiplier ideal sheaves. As applications, we generalize Koll'ar's torsion…

In this article, we present a concavity property of the minimal $L^{2}$ integrals related to multiplier ideal sheaves with Lebesgue measurable gain on weakly pseudoconvex K\"ahler manifolds. As applications, we give a necessary condition…

We establish a relative Bertini type theorem for multiplier ideal sheaves. Then we prove a relative version of the Koll\'ar--Nadel type vanishing theorem as an application.

In this paper, we obtain a Le Potier-type isomorphism theorem twisted with multiplier submodule sheaves, which relates a holomorphic vector bundle endowed with a strongly Nakano semipositive singular Hermitian metric to the tautological…

In this note, we present the concavity of the minimal $L^2$ integrals related to multiplier ideals sheaves on Stein manifolds. As applications, we obtain a necessary condition for the concavity degenerating to linearity, a characterization…

In this article, we present a concavity property of the minimal $L^2$ integrals related to multiplier ideal sheaves with Lebesgue measurable gain. As applications, we give necessary conditions for our concavity degenerating to linearity,…

This article discusses the geometric application of the method of multiplier ideal sheaves. It first briefly describes its application to effective problems in algebraic geometry and then presents and explains its application to the…

Let $X$ be a singular Hermitian complex space of pure dimension $n$. We use a resolution of singularities to give a smooth representation of the $L^2$-$\overline\partial$-cohomology of $(n,q)$-forms on $X$. The central tool is an…

A reduced divisor on a nonsingular variety defines the sheaf of logarithmic 1-forms. We introduce a certain coherent sheaf whose double dual coincides with this sheaf. It has some nice properties, for example, the residue exact sequence…

This paper describes how, in the case of algebraic surfaces, the well-known theorem of Donaldson-Uhlenbeck-Yau can be proved in a framework of generalized 'multiplier ideal sheaves', following the ideas of Siu. The key concept is that the…

The purpose of this survey is to present analytic versions of the injectivity theorem and their applications. The proof of our injectivity theorems is based on a combination of the L^2-method for the dbar-equation and the theory of harmonic…

We use a sheaf-theoretic approach to obtain a blow-up formula for Dolbeault cohomology groups with values in the holomorphic vector bundle over a compact complex manifold. As applications, we present several positive (or negative) examples…