相关论文: On the Iitaka Conjecture $C_{n,m}$ for K\"ahler Fi…

We show that a compact K\"ahler manifold $M$ containing a smooth connected divisor $D$ such that $M \setminus D$ is a homology cell, e.g., contractible, must be projective space with $D$ a hyperplane, provided $\dim M \not \equiv 3 \pmod…

In this paper we provide a positive answer to a conjecture due to A. J. Di Scala, A. Loi, H. Hishi (see [3, Conjecture 1]) claiming that a simply-connected homogeneous K\"ahler manifold M endowed with an integral K\"ahler form $\mu\omega$,…

We prove the Demailly--Peternell--Schneider conjecture in positive characteristic: if $X$ is a smooth projective variety over an algebraically closed field of characteristic $p>0$ with $-K_X$ is nef, then the Albanese morphism $a: X \to A$…

Let $M$ be a compact, holomorphic symplectic Kaehler manifold, and $L$ a non-trivial line bundle admitting a metric of semi-positive curvature. We show that some power of $L$ is effective. This result is related to the hyperkaehler SYZ…

We study the relationship between Iitaka fibrations and the conjecture on the existence of complements, assuming the good minimal model conjecture. In one direction, we show that the conjecture on the existence of complements implies the…

In this paper, we consider a proper K\"ahler fibration $f \colon X \to Y$ and a singular Hermitian line bundle $(L, h)$ on $X$ with semi-positive curvature. We prove that the direct image sheaf $f_{*}(\mathcal{O}_{X}(K_{X/Y}+L) \otimes…

As an application of the residue functions corresponding to the lc-measures developed by the authors, the proof of the injectivity theorem on compact K\"ahler manifolds for plt pairs by Matsumura is improved in this article to allow…

We prove that any compact K\"ahler 3-dimensional manifold which has no non-trivial complex subvarieties is a torus. This is a very special case of a general conjecture on the structure of 'simple manifolds', central in the bimeromorphic…

In this note we prove a conjecture of Kashiwara, which states that the Euler class of a coherent analytic sheaf F on a complex manifold X is the product of the Chern character of F with the Todd class of X. As a corollary, we obtain a…

Positiveness of scalar curvature and Ricci curvature requires vanishing the obstruction $\theta(M)$ which is computed in some KK-theory of C*-algebras index as a pairing of spin Dirac operator and Mishchenko bundle associated to the…

Vaisman's theorem for locally conformally K\"ahler (lcK) compact manifolds states that any lcK metric on a compact complex manifold which admits a K\"ahler metric is, in fact, globally conformally K\"ahler (gcK). In this paper, we extend…

In a previous paper, we proved that a projective K\"ahler manifold of positive total scalar curvature is uniruled. At the other end of the spectrum, it is a well-known theorem of Campana and Koll\'ar-Miyaoka-Mori that a projective K\"ahler…

If $f$ is an automorphism of a compact simply connected K\"ahler manifold with trivial canonical bundle that fixes a K\"ahler class, then the order of $f$ is finite. We apply this well known result to construct compact non-K\"ahler…

In the first part of this paper we revisit a classical topological theorem by Tischler (1970) and deduce a topological result about compact manifolds admitting a set of independent closed forms proving that the manifold is a fibration over…

This article has two purposes. In \cite{R3} (math.KT/0405211) we showed that the FIC (Fibered Isomorphism Conjecture for pseudoisotopy functor) for a particular class of 3-manifolds (we denoted this class by \cal C) is the key to prove the…

Firstly we show a generalization of the (1,1)-Lefschetz theorem for projective toric orbifolds and secondly we prove that on 2k-dimensional quasi-smooth hypersurfaces coming from quasi-smooth intersection surfaces, under the Cayley trick,…

It is well known that cohomology with compact supports is not a homotopy invariant but only a proper homotopy one. However, as the proper category lacks of general categorical properties, a Brown representability theorem type does not seem…

Two decades ago, as part of their work of generic vanishing theorems, Green-Lazarsfeld showed that over a compact Kahler manifold $X$, the cohomology jump loci in the $Pic^\tau(X)$ are all translates of subtori. In this paper, we generalize…

We develop in detail the theory of c-projective geometry, a natural analogue of projective differential geometry adapted to complex manifolds. We realise it as a type of parabolic geometry and describe the associated Cartan or tractor…

Given a family $f:\mathcal X \to S$ of canonically polarized manifolds, the unique K\"ahler-Einstein metrics on the fibers induce a hermitian metric on the relative canonical bundle $\mathcal K_{\mathcal X/S}$. We use a global elliptic…