Related papers: On the Kodaira dimension
We prove several results on the additivity of Kodaira dimension under smooth morphisms of smooth projective varieties.
I propose a few increasingly stronger "superadditivity" conjectures regarding the behavior of Kodaira dimension under morphisms of smooth quasi-projective complex varieties.
This is a survey on the various notions of Kodaira dimension in low dimensional topology. The focus is on progress after the 2006 survey [78].
In this short note, we determine the Kodaira dimension and some of the plurigenera of (a desingularization of) a symmetric power of a smooth projective variety. We use it to obtain bounds on the genus of curve passing through a fixed number…
A Kodaira fibration is a compact, complex surface admitting a holomorphic submersion onto a complex curve, such that the fibers have nonconstant moduli. We consider Kodaira fibrations X with nontrivial invariant rational cohomology in…
Two conjectures relating the Kodaira dimension of a smooth projective variety and existence of number of nowhere vanishing 1-forms on the variety are proposed and verified in dimension 3.
We study the behavior of the Kodaira dimension of algebraic fiber spaces over threefolds. We prove some cases of the Iitaka Conjecture $C_{n,3}$, including certain situations where the base variety is a Calabi--Yau threefold.
We introduce an axiomatic definition for the Kodaira dimension and classify Thurston geometries in dimensions $\leq 5$ in terms of this Kodaira dimension. We show that the Kodaira dimension is monotone with respect to the partial order…
We prove that a general hyperplane section of a smooth Legendrian subvariety in a projective space admits Legendrian embedding into another projective space. This gives numerous new examples of smooth Legendrian subvarieties, some of which…
In this paper, we will prove subadditivity of Kodaira dimensions for a fibration with possibly singular geometric generic fiber, under certain nefness and relative semi-ampleness conditions. As an application, for a fibration $f: X \to Y$…
The aim of this paper is to continue the study of Kodaira dimension for almost complex manifolds, focusing on the case of compact $4$-dimensional solvmanifolds without any integrable almost complex structure. According to the classification…
We prove the invariance of plurigenera under smooth projective deformations of varieties with nonnegative Kodaira dimensions.
It is shown that a complex normal projective variety has non-positive Kodaira dimension if it admits a non-isomorphic quasi-polarized endomorphism. The geometric structure of the variety is described by methods of equivariant lifting and…
We prove the deformation invariance of Kodaira dimension and of certain plurigenera for log surfaces which are smooth over a DVR.
We give a proof of the Kodaira vanishing theorem on smooth complex surfaces using geometric stability conditions. Likewise, we give a new proof of a result of Xie characterizing the counterexamples of the Kodaira vanishing theorem in…
We show that for a surjective, separable morphism f of smooth projective varieties over an algebraically closed field of positive characteristic such that $f_* \mathcal{O}_X = \mathcal{O}_Y$ subadditivity of Kodaira dimension holds,…
In complex geometry a classical and useful invariant of a complex manifold is its Kodaira dimension. Since its introduction by Iitaka in the early 70's, its behavior under deformations was object of study and it is known that Kodaira…
We study the Kodaira dimension of almost complex manifolds admitting an $\mathrm{SU} (m)$-structure. We introduce the notion of almost complex structure of splitting type and of associated $\mathrm{SU} (m)$-structure. When the latter is…
We describe explicitly the possible degenerations of a class of double Kodaira fibrations in the moduli space of stable surfaces. Using deformation theory we also show that under some assumptions we get a connected component of the moduli…
In this note we discuss the effect of the symplectic sum along spheres in symplectic four-manifolds on the Kodaira dimension of the underlying symplectic manifold. We find that the Kodaira dimension is non-decreasing. Moreover, we are able…