Related papers: Kodaira Dimension of Subvarieties

Given a positive singular hermitian metric of a pseudoeffective line bundle on a complex Kaehler manifold, a singular foliation is constructed satisfying certain analytic analogues of numerical conditions. This foliation refines Tsuji's…

Let $X$ be a complex quasiprojective variety. A result of Noguchi-Winkelmann-Yamanoi shows that if $X$ admits a Zariski dense entire curve, then its quasi-Albanese map is a fiber space. We show that the orbifold structure induced by a…

A stratified pseudomanifold is normal if its links are connected. A normalization of a stratified pseudomanifold $X$ is a normal stratified pseudomanifold $Y$ together with a finite-to-one projection $n:Y\to X$ satisfying a local condition…

Fujita's second theorem for K\"ahler fibre spaces over a curve asserts that the direct image $V$ of the relative dualizing sheaf splits as the direct sum $ V = A \oplus Q$, where $A$ is ample and $Q$ is unitary flat. We focus on our…

We show that if $f\colon X \to T$ is a surjective morphism between smooth projective varieties over an algebraically closed field $k$ of characteristic $p>0$ with geometrically integral and non-uniruled generic fiber, then $K_{X/T}$ is…

A general fiber of the Gauss map of a projective variety in $\mathbb{P}^N$ coincides with a linear subvariety of $\mathbb{P}^N$ in characteristic zero. In positive characteristic, S. Fukasawa showed that a general fiber of the Gauss map can…

In this expository article, we prove a birational classification of smooth projective models of surfaces with negative Kodaira dimension over $\mathbb{Z}$ and over more general rings of integers $\mathcal{O}_K$, depending on their…

Let $X$ be a smooth projective horospherical variety of Picard number one. We show that a uniruled projective manifold of Picard number one is biholomorphic to $X$ if its variety of minimal rational tangents at a general point is…

For a local complete intersection subvariety $X=V({\mathcal I})$ in ${\mathbb P}^n$ over a field of characteristic zero, we show that, in cohomological degrees smaller than the codimension of the singular locus of $X$, the cohomology of…

In this paper, we prove a positive characteristic analog of Nakayama's inequality on the numerical Kodaira dimension of algebraic fiber spaces when the generic fibers have nef canonical divisors. To this end, we establish variants of Popa…

We study pluricanonical systems on smooth projective varieties of positive Kodaira dimension, following the approach of Hacon-McKernan, Takayama and Tsuji succesfully used in the case of varieties of general type. We prove a uniformity…

The paper studies the deformation theory of a holomorphic surjective map from a normal compact complex space to a compact Kaehler manifold and describes the component of the space of holomorphic maps, generalizing results in the projective…

In this paper we prove the birational superrigidity of Fano-Mori fibre spaces $\pi\colon V\to S$, every fibre of which is a complete intersection of type $d_1\cdot d_2$ in the projective space ${\mathbb P}^{d_1+d_2}$, satisfying certain…

It is a conjecture of Koll\'ar that a variety $X$ with rational singularities in some open subvariety $U$ has a rationalification; that is, a proper, birational morphism $f: Y \rightarrow X$ such that $Y$ has rational singularities, and…

In this note we are going to prove that if we have a fibration of smooth projective varieties $X\to S$ over a surface $S$ such that $X$ is of dimension four and that the geometric generic fiber has finite dimensional motive and the first…

We prove the invariance of plurigenera under smooth projective deformations of varieties with nonnegative Kodaira dimensions.

By a $B$-regular variety, we mean a smooth projective variety over $C$ admitting an algebraic action of the upper triangular Borel subgroup $B \subset SL_2(C)$ such that the unipotent radical in $B$ has a unique fixed point. A result of M.…

Let $(M^{n},g)$ be a closed, connected, oriented, $C^{\infty}$, Riemannian, n-manifold with a transversely oriented foliation $\boldkey F$. We show that if $\lbrace X,Y \rbrace$ are basic vector fields, the leaf component of $[X,Y]$,…

Let $X$ be a minimal projective Gorenstein 3-fold of general type. We give two applications of an inequality between $\chi (\omega_X)$ and $p_g(X)$: 1) Assume that the canonical map $\Phi_{|K_X|}$ is of fiber type. Let $F$ be a smooth model…

We provide a characterization of parallelizable compact complex manifolds and their quotients using holomorphic symmetric differentials. In particular we show that compact complex manifolds of Kodaira dimension 0 having strongly semiample…