Related papers: Volumes on Complex Analytic Spaces

The goals of this paper are of two aspects. Firstly, we introduce the notion of generalized numerical Kodaira dimension with multiplier ideal sheaf and establish the subadditivity inequalities in terms of this notion, which can be used to…

In this paper we investigate boundedness and volumes of generalised pairs, and give applications to usual pairs especially to a class of pairs that we call stable log minimal models. Fixing the dimension and a DCC set controlling…

We extend previous results on boundedness of sets of coherent sheaves on a compact K\"ahler manifold to the relative and not necessarily smooth case. This enlarged context allows us to prove properness properties of the relative Douady…

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…

We consider the moduli space of the extremal K\"ahler metrics on compact manifolds. We show that under the conditions of two-sided total volume bounds, $L^{n\over2}$-norm bounds on $\Riem$, and Sobolev constant bounds, this Moduli space can…

We prove an analogue of Fujino and Mori's ``bounding the denominators'' in the log canonical bundle formula (see also Prokhorov and Shokurov) for Kawamata log terminal pairs of relative dimension one. As an application we prove that for a…

Let $(X,g)$ be a compact Riemannian manifold with quasi-positive Riemannian scalar curvature. If there exists a complex structure $J$ compatible with $g$, then the canonical bundle $K_X$ is not pseudo-effective and the Kodaira dimension…

In this paper, we investigate Kondratiev spaces on domains of polyhedral type. In particular, we will be concerned with necessary and sufficient conditions for continuous and compact embeddings, and in addition we shall deal with pointwise…

Let $\pi:X\to Y$ be an $n$-dimensional iterated Kodaira fibration with fiber of genus $g$ and injective monodromy. Llosa Isenrich and Py proved that we can pass to a finite index subgroup of $\pi_1(X)$ to get the base space of an…

It is in general unknown which topological complex vector bundles on a non-algebraic surface admit holomorphic structures. We solve this problem for primary Kodaira surfaces by using results of Kani on curves of genus two with elliptic…

We study the positivity of CM line bundles on the coarse moduli space of Kawamata log terminal (klt) good minimal models with Kodaira dimension one. We prove that the seminormalization of the moduli space is quasi-projective under a mild…

Let $(L,he^{-u})$ be a pseudoeffective line bundle on an $n$-dimensional compact K\"ahler manifold $X$. Let $h^0(X,L^k\otimes \mathcal I(ku))$ be the dimension of the space of sections $s$ of $L^k$ such that $h^k(s,s)e^{-ku}$ is integrable.…

In this paper, we construct counterexamples to the boundedness of generalised log canonical models of surfaces with fixed appropriate invariants, where the underlying varieties can have arbitrary Kodaira dimension. This answers a question…

This paper has two goals. The first is to present the construction, due to the author, of measures on non-archimedean analytic varieties associated to metrized line bundles and some of its applications. We take this opportunity to add…

We introduce and study the restricted volume of a divisor along a subvariety. Our main result is a description of the irreducible components of the augmented base locus by the vanishing of the restricted volume.

We prove an additivity result for the log Kodaira dimension of algebraic fiber spaces over abelian varieties, a superadditivity result for fiber spaces over varieties of maximal Albanese dimension, as well as a subadditivity result for log…

We continue previous works by various authors and study the birational geometry of moduli spaces of stable rank-two vector bundles on surfaces with Kodaira dimension $-\infty$. To this end, we express vector bundles as natural extensions,…

Let X be a polyhedral complex with finitely many isometry classes of links. We establish a restriction on the covolumes of uniform lattices acting on X. When X is two-dimensional and has all links isometric to either a complete bipartite…

We prove that the variation in a smooth projective family of varieties admitting a good minimal model forms a lower bound for the Kodaira dimension of the base, if the dimension of the base is at most five and its Kodaira dimension is…

We study the Kodaira dimension of the compactified n-fold Kuga variety over the moduli space of principally polarised abelian g-folds. We construct a suitable compactification, which we call a Namikawa compactification, and show that in…