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

Let $M^n$ be a complete noncompact K\"ahler manifold with nonnegative bisectional curvature and maximal volume growth, we prove that $M$ is biholomorphic to $\mathbb{C}^n$. This confirms Yau's uniformization conjecture when M has maximal…

In this paper, we study MRC fibrations of compact K\"ahler manifolds with partially semi-positive curvature. We first prove that a compact K\"ahler manifold is rationally connected if its tangent bundle is BC-$p$ positive for all $1\leq…

We explain a correct proof of the decomposition theorem for direct images of constant Hodge modules by proper K\"ahler morphisms of complex manifolds. We also give some examples showing certain difficulty in the non-constant Hodge module…

Let X be a compact K\"ahler manifold such that the universal cover admits a compactification. We conjecture that the fundamental group is almost abelian and reduce it to a classical conjecture of Iitaka.

We develop some results on the positivity of direct image bundles in the particular case of a trivial fibration over a one-dimensional base. We also apply the results to study variations of Kahler metrics.

We treat Koll\'ar's injectivity theorem from the analytic (or differential geometric) viewpoint. More precisely, we give a curvature condition which implies Koll\'ar type cohomology injectivity theorems. Our main theorem is formulated for a…

In arXiv:1911.08213 it was conjectured that the compactly supported cohomology of the $m$-th restricted contact locus of an isolated hypersurface singularity coincides, up to a shift, with the Floer cohomology of the $m$-th iterate of the…

Based on results by S.K. Roushon (math.KT/0408243 and math.KT/0405211) this thesis summarizes in an axiomatic way when a Meta-Isomorphism-Conjecture in the sense of Lueck and Reich (math.KT/0402405) is true for fundamental groups of…

In this paper, we prove that a compact K\"ahler manifold $X$ with semi-positive holomorphic sectional curvature admits a locally trivial fibration $\phi \colon X \to Y$, where the fiber $F$ is a rationally connected projective manifold and…

We show that for any complete connected K\"ahler manifold the index of the group of complex affine transformations in the group of c-projective transformations is at most two unless the K\"ahler manifold is isometric to complex projective…

In this paper, we prove that a compact K\"ahler manifold $X$ with the nef anti-canonical bundle $-K_{X}$ admits a locally trivial fibration $\phi \colon X \to Y$, where the fiber $F$ is a rationally connected manifold and the base $Y$ is a…

We show that techniques inspired by Koll\'ar and Viehweg's study of weak positivity, combined with vanishing theorems for log-canonical pairs, lead to new consequences regarding generation and vanishing properties for direct images of…

Using the method of Coand\u{a} and Trautmann (2006), we give a simple proof of the following theorem due to Tyurin (1976) in the smooth case: if a vector bundle $E$ on a $c$-codimensional locally Cohen-Macaulay closed subscheme $X$ of the…

We first provide details for the proof of Fujita's second theorem for K\"ahler fibre spaces over a curve, asserting that the direct image $V$ of the relative dualizing sheaf splits as the direct sum $ V = A \oplus Q$, where $A$ is ample and…

Let $(X,D)$ be a log-canonical (lc) pair, in which $X$ is a compact K\"ahler manifold and $D$ is a reduced snc divisor, and let $F$ be a holomorphic line bundle on $X$ equipped with a smooth metric $h_F = e^{-\varphi_F}$. Via the use of the…

In this short note we prove the Iitaka C_nm conjecture for algebraic fiber spaces over surfaces

The `Folk Theorem' that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type is proved in the context of manifolds with corners. This procedure is shown to capture the…

Let $L$ be a holomorphic line bundle on a hyperkahler manifold $M$, with $c_1(L)$ nef and not big. SYZ conjecture predicts that $L$ is semiample. We prove that this is true, assuming that $(M,L)$ has a deformation $(M',L')$ with $L'$…

We study the conditions under which a K\"ahlerian structure $(G,J)$ of general natural lift type on the cotangent bundle $T^*M$ of a Riemannian manifold $(M,g)$ has constant holomorphic sectional curvature. We obtain that a certain…

A basic problem in the classification theory of compact complex manifolds is to give simple characterizations of complex tori. It is well known that a compact K\"ahler manifold $X$ homotopically equivalent to a a complex torus is…