Related papers: Skoda's $L^2$ division theorem for $L^2$-optimal p…
We prove new Skoda-type division, or ideal membership, theorems. We work in a geometric setting of line bundles over Kahler manifolds that are Stein away from an analytic subvariety. (This includes complex projective manifolds.) Our…
In this paper, we prove a Skoda type division theorem with sharp $L^2$-estimate. Furthermore, using this estimate, we provide new characterizations of plurisubharmonic functions. We also explain that the sharp $L^2$-division theorem leads…
In this paper, we present a converse to a version of Skoda's $L^2$ division theorem by investigating the solvability of $\bar{\partial}$ equations of a specific type.
In this paper, we show that the $L^2$-optimal condition implies the $L^2$-divisibility of $L^2$-integrable holomorphic functions. As an application, we offer a new characterization of bounded $L^2$-domains of holomorphy with null thin…
We first present a Skoda type division theorem for holomorphic sections of line bundles on a projective variety which is essentially the most general, compared to previous ones. It is derived from Varolin's theorem as a corollary. Then we…
We prove a Skoda-type division theorem via a degeneration argument. The proof is inspired by B. Berndtsson and L. Lempert's approach to the $L^2$ extension theorem and is based on positivity of direct image bundles. The same tools are then…
We present a short proof of a version of the Ohsawa-Takegoshi-Manivel $L^2$ extension theorem as a corollary of a Skoda-type $L^2$ division theorem with bounded generators. The new division theorem is of independent interest: the…
In this article, we obtain an Ohsawa-Takegoshi-type $L^2$-extension for upper semi-continuous $L^2$-optimal functions via a Lebesgue-type differentiation theorem. As applications, we give a characterization of plurisubharmonic functions via…
Skoda's 1972 result on ideal generation is a crucial ingredient in the analytic approach to the finite generation of the canonical ring and the abundance conjecture. Special analytic techniques developed by Skoda, other than applications of…
We establish a twisted version of Skoda's estimate for the Koszul complex from which we get division theorems for the Koszul complex. This generalizes Skoda's division theorem. We also show how to use Skoda triples to produce division…
Under certain integrability and geometric conditions, we prove division theorems for the exact sequences of holomorphic vector bundles and improve the results in the case of Koszul complex. By introducing a singular Hermitian structure on…
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 give new a proof of the general Brian\c{c}on-Skoda theorem about ideals of holomorphic functions by means of multivariable residue calculus. The method gives new variants of this theorem for products of ideals. Moreover, we obtain a…
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…
We prove an $L^2$ extension theorem of Ohsawa-Takegoshi type for extending holomorphic sections of line bundles from a subvariety which is given as a maximal log-canonical center of a pair and is of general codimension in a projective…
We study the following optimal $L^2$ extension problem of openness type: given a complex manifold $M$, a closed subvariety $S\subset M$ and a holomorphic vector bundle $E\rightarrow M$, for any $L^2$ holomorphic section $f$ defined on some…
We deal with the distributions of holomorphic curves and integral points off divisors. We will simultaneouly prove an optimal dimension estimate from above of a subvariety W off a divisor D which contains a Zariski dense entire holomorphic…
Like categories, small 2-categories have well-understood classifying spaces. In this paper, we deal with homotopy types represented by 2-diagrams of 2-categories. Our results extend to homotopy colimits of 2-functors lower categorical…
We establish a generalization of the Briancon-Skoda theorem about integral closures of ideals for graded systems of ideals satisfying a certain geometric condition.
We study the Stokes phenomenon for the solutions of general homogeneous linear moment partial differential equations with constant coefficients in two complex variables under condition that the Cauchy data are holomorphic on the complex…