Related papers: On the Kodaira dimension

We introduce a refinement of the Gorenstein flat dimension for complexes over an associative ring--the Gorenstein flat-cotorsion dimension--and prove that it, unlike the Gorenstein flat dimension, behaves as one expects of a homological…

Given a (meromorphic) fibration $f:X\to Y$ where $X$ and $Y$ are compact complex manifolds of dimensions $n$ and $m$, we define $L_f$ to be the invertible subsheaf of the sheaf of holomorphic $m$-forms of $X$ given by the saturation of…

Modulo trivial exceptions, we show that smoothly nontrivial symplectic sums of symplectic 4-manifolds along surfaces of positive genus are never rational or ruled, and we enumerate each case in which they have Kodaira dimension zero (i.e.,…

We point out a gap in Murre's proof of the existence of a universal regular homomorphism for codimension $2$ cycles on a smooth projective variety, and offer two arguments to fill this gap.

We study homological invariants of smooth families of real quadratic forms as a step towards a "Lagrange multipliers rule in the large" that intends to describe topology of smooth maps in terms of scalar Lagrange functions.

In this paper, we study the differential smoothness of 3-dimensional skew polynomial algebras and diffusion algebras.

We define the Kodaira dimension for $3$-dimensional manifolds through Thurston's eight geometries, along with a classification in terms of this Kodaira dimension. We show this is compatible with other existing Kodaira dimensions and the…

Following the first paper, we continue to study Mori extractions from singular curves centred in a smooth 3-fold. We treat the case where the divisorial extraction exists in relative codimension at most 3.

Kodaira fibred surfaces are a remarkable example of projective classifying spaces, and there are still many intriguing open questions concerning them, especially the slope question. The topological characterization of Kodaira fibrations is…

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 use filtered log-$\mathscr{D}$-modules to represent the (dual) localization of Saito's Mixed Hodge Modules along a smooth hypersurface, and show that they also behave well under the direct image functor and the dual functor in the…

We discuss rigid compact complex manifolds of Kodaira dimension 1, arising as product-quotient varieties. First, we show that there is no free rigid action on the product of $(n-1)$ elliptic curves and a curve of genus at least two. Then,…

This note contains some results related to the definitions of toroidal embeddings and toroidal morphisms over non-closed fields of characteristic zero.

The paper is concerned with `geometrization' of smooth (i.e. with open stabilizers) representations of the automorphism group of universal domains, and with the properties of `geometric' representations of such groups. As an application, we…

We give a bound on the H-constants of configurations of smooth curves having transversal intersection points only on an algebraic surface of non-negative Kodaira dimension. We also study in detail configurations of lines on smooth complete…

In this article we study how the birational geometry of a normal projective variety $X$ is influenced by a normal subvariety $A \subset X.$ One of the most basic examples in this context is provided by the following situation. Let $f:X\to…

We develop a moduli theory of algebraic varieties and pairs of non-negative Kodaira dimension. We define stable minimal models and construct their projective coarse moduli spaces under certain natural conditions. This can be applied to a…

The fundamental group of a smooth projective variety is fibered if it maps onto the fundamental group of smooth curve of genus 2 or more. The goal of this paper is to establish some strong restrictions on these groups, and in particular on…

This paper deals with continuous and compact mappings of the Fourier transform in function spaces with dominating mixed smoothness.

We describe the equivariant cobordism ring of smooth toric varieties. This equivariant description is used to compute the ordinary cobordism ring of such varieties.