相关论文: Double Kodaira fibrations

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…

Kodaira fibrations are surfaces of general type with a non-isotrivial fibration, which are differentiable fibre bundles. They are known to have positive signature divisible by $4$. Examples are known only with signature 16 and more. We…

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…

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 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…

We exhibit new examples of double Kodaira fibrations by using finite Galois covers of a product $\Sigma_b \times \Sigma_b$, where $\Sigma_b$ is a smooth projective curve of genus $b \geq 2$. Each cover is obtained by providing an explicit…

Being inspired by Ross' construction of unstable products of certain smooth curves, we show that the product $C\times C$ of every smooth curve $C$ of genus at least 2 is not slope semistable with respect to certain polarisations. Besides,…

We consider fibrations of genus 2 over complex surfaces. The purpose of this paper is primarily to provide a geometric description of the possible structures of the fibration on a neighborhood of a singular fiber. In particular it is shown…

Kodaira fibrations have non-trivial vertical fundamental groups and their slopes are all $12$. In this paper, we show that $12$ is indeed the sharp upper bound for the slopes of fibrations with trivial vertical fundamental groups.…

We consider the K3 surfaces that arise as double covers of the elliptic modular surface of level 5, $R_{5,5}$. Such surfaces have a natural elliptic fibration induced by the fibration on $R_{5,5}$. Moreover, they admit several other…

We study several geometric and group theoretical problems related to Kodaira fibrations, to more general families of Riemann surfaces, and to surface-by-surface groups. First we provide constraints on Kodaira fibrations that fiber in more…

Let $S \to C$ be a Kodaira fibration. Here we show that whether or not the algebraic surface $S$ is defined over a number field depends only on the biholomorphic class of its universal cover.

Given a relatively minimal non locally trivial fibred surface f: S->B, the slope of the fibration is a numerical invariant associated to the fibration. In this paper we explore how properties of the general fibre of $f$ and global…

The fundamental group $\pi$ of a Kodaira fibration is, by definition, the extension of a surface group $\Pi_b$ by another surface group $\Pi_g$, i.e. \[ 1 \rightarrow \Pi_g \rightarrow \pi \rightarrow \Pi_b \rightarrow 1. \] Conversely, we…

We introduce some special presentations on finite groups, that we call "diagonal double Kodaira structures" and whose existence is equivalent to the existence of some special Kodaira fibred surfaces, that we call "diagonal double Kodaira…

In the present paper we consider fibrations $f: S \ra B$ of an algebraic surface onto a curve $B$, with general fibre a curve of genus $g$. Our main results are: 1) A structure theorem for such fibrations in the case $g=2$ 2) A structure…

We prove that any two-dimensional moduli space of stable 2-vector bundles, in the non-filtrable range, on a primary Kodaira surface is a primary Kodaira surface. If a universal bundle exists, then the two surfaces are homeomorphic up to…

In this paper, we study the structure, deformations and the moduli spaces of complex projective surfaces admitting genus two fibrations over elliptic curves. We observe that, a surface admitting a smooth fibration as above is elliptic and…

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…

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 $f: X \to Y$…