相关论文: Bergman kernels and the pseudoeffectivity of relat…

The goal of this work is to pursue the study of pseudo-effective line bundles and vector bundles. Our first result is a generalization of the Hard Lefschetz theorem for cohomology with values in a pseudo-effective line bundle. The Lefschetz…

Our main goal in this article is to establish a quantitative version of the positivity properties of twisted relative pluricanonical bundles and their direct images. The notion of "singular Hermitian metric" on vector bundles (together with…

Generalizing the recent result of Berndtsson, we prove the Nakano semipositivity of the direct image of relative pluricanonical systems and the direct image of relative adjoint (singular) hermitian line bundle with semipositive curvature.…

In this paper, we develop the theory of singular hermitian metrics on vector bundles. As an application, we give a structure theorem of a projective manifold $X$ with pseudo-effective tangent bundle: $X$ admits a smooth fibration $X \to Y$…

In earlier work the authors proved the Bergman kernel expansion for semipositive line bundles over a Riemann surface whose curvature vanishes to atmost finite order at each point. Here we explore the related results and consequences of the…

In this paper, we show an extension type theorem for twisted pluricanonical sections on a family of smooth projective manifolds (the twisting line bundle being pseudo-effective and having a prescribed multiplier ideal on the central fiber).

We give an extensive study on the Bergman kernel expansions and the random zeros associated with the high tensor powers of a semipositive line bundle on a complete punctured Riemann surface. We prove several results for the zeros of…

We discuss the local freeness and the numerical semipositivity of direct images of relative pluricanonical bundles for surjective morphisms between smooth projective varieties with connected fibers. We give a desirable semipositivity…

Contents 1. Algebraicity criterion: statement 2. Proof of the algebraicity criterion. 3. Pseudoeffectivity and movable classes. 4. Harder-Narasimhan filtrations and pseudo-effectivity. 5. Pseudo-effectivity of relative canonical bundles. 6.…

Let X be a strictly pseudoconcave domain in a closed polarized complex manifold (Y,L) where L is a (semi-)positive line bundle over Y. Any given Hermitian metric on L, together with a volume form, induces by restriction to X a Hilbert space…

We generalize the results of Montgomery for the Bochner Laplacian on high tensor powers of a line bundle. When specialized to Riemann surfaces, this leads to the Bergman kernel expansion and geometric quantization results for semi-positive…

We prove an effective vanishing theorem for direct images of log pluricanonical bundles of projective semi-log canonical pairs. As an application, we obtain a semipositivity theorem for direct images of relative log pluricanonical bundles…

The goal of this survey is to present various results concerning the cohomology of pseudoeffective line bundles on compact K{\"a}hler manifolds, and related properties of their multiplier ideal sheaves. In case the curvature is strictly…

We give new characterizations of plurisubharmonic functions and Griffiths positivity of holomorphic vector bundles with singular Finsler metrics. As applications, we present a different method to prove plurisubharmonic variation of…

We shall give an explicit estimate of the lower bound of the Bergman kernel associated to a positive line bundle. In the compact Riemann surface case, our result can be seen as an explicit version of Tian's partial $C^0$-estimate.

In this paper, we give complex geometric descriptions of the notions of algebraic geometric positivity of vector bundles and torsion-free coherent sheaves, such as nef, big, pseudo-effective and weakly positive, by using singular Hermitian…

We prove approximation results about sequences of Berezin transforms of finite sums of finite product of Toeplitz operators (and bounded linear maps, in general) in the spirit of Ramadanov and Skwarczynski theorems that are about…

We introduce a new class of canonical AZD's (called the supercanonical AZD's) on the canonical bundles of smooth projective varieties with pseudoeffective canonical classes. We study the variation of the supercanonical AZD $\hat{h}_{can}$…

We prove an exponential estimate for the asymptotics of Bergman kernels of a positive line bundle under hypotheses of bounded geometry. We give further Bergman kernel proofs of complex geometry results, such as separation of points,…

In this paper we study the positivity of the cotangent bundle of projective manifolds. We conjecture that the cotangent bundle is pseudoeffective if and only the manifold has non-zero symmetric differentials. We confirm this conjecture for…