Related papers: On the Kodaira dimension

The coarsening process in a class of driven systems is studied. These systems have previously been shown to exhibit phase separation and slow coarsening in one dimension. We consider generalizations of this class of models to higher…

This paper was inspired by work by T. Peternell, M. Schneider and A.J. Sommese on the Kodaira dimension of subvarieties. In it I find a relation between the Kodaira-Iitaka dimension of a divisor on a normal variety and that of related…

We explore the relationship between fibrations arising naturally from a surjective morphism to an abelian variety. These fibrations encode geometric information about the morphism. Our study focuses on the interplay of these fibrations and…

This is a survey on symplectic birational geometry. In arbitrary dimension, this subject is centered around the notion of uniruledness. In low dimensions, we will also discuss Kodaira dimension and minimality.

In this paper, we prove a result related to the deformation of complex submanifolds, modifying a result of Kodaira (Ann. Math, 75(1), 146-162, 1962).

The notion of Kodaira dimension has recently been extended to general almost complex manifolds. In this paper we focus on the Kodaira dimension of almost K\"ahler manifolds, providing an explicit computation for a family of almost K\"ahler…

In this paper we try to introduce a good smoothness notion for a functor. We consider properties and conditions from geometry and algebraic geometry which we expect a smooth functor should to have.

A class of solid-on-solid growth models with short range interactions and sequential updates is studied. The models exhibit both smooth and rough phases in dimension d=1. Some of the features of the roughening transition which takes place…

In this paper we investigate the Kodaira dimension of almost complex $4$-manifolds with torsion first Chern class. First, we prove that, if the almost complex structure is also tamed, the only possible values for the Kodaira dimension are…

In this paper we study flatness of the restriction on some special subgerms (e.g. the reduction and the unmixed part) of the total space of a flat morphism over a smooth base space. We give a relationship between reducedness of the total…

We study the space of deformations of a smooth foliation of the 5-sphere by complex manifolds

This is the first of a series of papers, in which we study the plurigenera, the Kodaira dimension and more generally the Iitaka dimension on compact almost complex manifolds. Based on the Hodge theory on almost complex manifolds, we…

The moduli space of (1,p)-polarized abelian surfaces is a quasi-projective variety. In the case when p is a prime, we study its Kodaira dimension. We show that it is of general type for p > 71 and some smaller values of p. This improves an…

We discuss various aspects of noncommutative geometry of a smooth subalgebra of the Toeplitz algebra. In particular, we study the structure of derivations on this subalgebra.

We give a bimeromorphic classification of compact K\"ahler manifolds of Kodaira codimension one that admit a holomorphic one form without zeros.

We introduce the Kodaira dimension of contact 3-manifolds and establish some basic properties. In particular, contact 3-manifolds with distinct Kodaria dimensions behave differently when it comes to the geography of various kinds of…

Given two nonsingular real algebraic varieties V and W, we consider the problem of deciding whether a smooth map f: V -> W can be approximated by regular maps in the space of smooth maps from V to W. Our main result is a complete solution…

A Kodaira fibration is a non-isotrivial fibration $f\colon S\rightarrow B$ from a smooth algebraic surface $S$ to a smooth algebraic curve $B$ such that all fibers are smooth algebraic curves of genus $g$. Such fibrations arise as complete…

We establish the deformation theory of Lie groupoid morphisms, describe the corresponding deformation cohomology of morphisms, and show the properties of the cohomology. We prove its invariance under isomorphisms of morphisms. Additionally,…

This essay summarizes the state of the art on some aspects of the dynamics of polynomial diffeomorphsms in complex dimension two, and it presents a number of open questions.