Related papers: On the Kodaira problem for uniruled K\"ahler space…

For a homogeneous space X (not necessarily principal) of a connected algebraic group G (not necessarily linear) over a number field k, we prove a theorem of strong approximation for the adelic points of X in the Brauer-Manin set. Namely,…

Given a compact complex manifold X of dimension n, we define a bimeromorphic invariant $\kappa_+(X)$ as the maximum p for which there is a saturated line subsheaf L of the sheaf of holomorphic p forms whose Kodaira dimension $\kappa (L)$…

For every fibration $f : X \to B$ with $X$ a compact K\"ahler manifold, $B$ a smooth projective curve, and a general fiber of $f$ an abelian variety, we prove that $f$ has an algebraic approximation.

We show, using [14], that a smooth projective fibration f : X $\rightarrow$ Y between connected complex quasi-projective manifolds satisfies the equality $\kappa$(X) = $\kappa$(X y) + $\kappa$(Y) of Logarithmic Kodaira dimensions if its…

We describe a method to construct completions of affine spaces into total spaces of $\mathbb{Q}$-factorial terminal Mori fiber spaces over the projective line. As an application we provide families of examples with non-rational,…

Let $X$ denote the complex projective plane, blown up at the nine base points of a pencil of cubics, and let $D$ be any fiber of the resulting elliptic fibration on $X$. Using ansatz metrics inspired by work of Gross-Wilson and a PDE method…

We study the Kodaira dimension of a real parallelizable manifold $M$, with an almost complex structure $J$ in standard form with respect to a given parallelism. For $X = (M, J)$ we give conditions under which $\operatorname{kod}(X) = 0$. We…

We provide infinitely many examples of pairs of diffeomorphic, non simply connected K\" ahler manifolds of complex dimension three with different Kodaira dimensions. Also, in any possible Kodaira dimension we find infinitely many pairs of…

We show that badly approximable matrices are exactly those that, for any inhomogeneous parameter, can not be inhomogeneous approximated at every monotone divergent rate, which generalizes Ram\'irez's result (2018). We also establish some…

We propose an exactly-solvable model of the quantum oscillator on the class of K\"ahler spaces (with conic singularities), connected with two-dimensional complex projective spaces. Its energy spectrum is nondegenerate in the orbital quantum…

We first provide details for the proof of Fujita's second theorem for K\"ahler fibre spaces over a curve, asserting that the direct image $V$ of the relative dualizing sheaf splits as the direct sum $ V = A \oplus Q$, where $A$ is ample and…

We show that there exist Mori fibre spaces whose total spaces are klt but bases are not. We also construct Mori fibre spaces which have relatively non-trivial torsion line bundles.

For the twistor spaces of the Bochner-K\"ahler manifold $M = H^l \times P^n$, systems of holomorphic coordinates are constructed. As an application of them, an explicit description of the moduli space of relative deformations of fibers of…

In the moduli space of polarized varieties the same unpolarized variety can occur multiple times However, for K3 surfaces, compact hyperk\"ahler manifolds, and abelian varieties the number is finite. This may be viewed as a consequence of…

We show that the almost complex Hodge number $h^{0,1}$ varies with different choices of almost K\"ahler metrics. This answers the almost K\"ahler version of a question of Kodaira and Spencer.

We give a simple proof of why there is a Matrix theory approximation for a membrane shaped like an arbitrary Riemann surface. As corollaries, we show that noncompact membranes cannot be approximated by matrices and that the Poisson algebra…

We study the effect of mirror symmetry for K3 surfaces on D-brane probe physics. The case of elliptically fibered K3 surfaces is considered in detail. In many cases, mirror can transform a singular fiber of Kodaira's type ADE into sets of…

Let $k$ be a number field and let $T$ be a $k$-torus. Consider a fibration in torsors under $T$, i.e. a morphism $f: X \to \mathbb{P}^1_k$ from a smooth, projective $k$-variety $X$ to $\mathbb{P}^1_k$ such that the generic fibre $X_\eta \to…

Over any algebraically closed field of positive characteristic, we construct examples of fibrations violating subadditivity of Kodaira dimension.

Moduli spaces of stably irreducible sheaves on Kodaira surfaces belong to the short list of examples of smooth and compact holomorphic symplectic manifolds, and it is not yet known how they fit into the classification of holomorphic…