Related papers: Marked Godeaux surfaces with special bicanonical f…

We study the extension of a hyperelliptic K3 surface to a Fano 6-fold. This determines a family of surfaces of general type with p_g=1, K^2=2 and hyperelliptic canonical curve, where each surface is a weighted complete intersection inside a…

Using elementary methods of algebraic geometry, we present constructions of hyperelliptically fibred surfaces containing nodal fibres.

In this paper we describe a construction method for numerical Godeaux surfaces based on homological algebra. We show the existence of an 8-dimensional locally complete family of simply connected numerical Godeaux surfaces.

We present a computational method for detecting highly singular members in families of algebraic varieties. Applying this approach to a family of numerical Godeaux surfaces, we obtain explicit examples with many singularities. In…

We prove that Godeaux--Reid surfaces with torsion group Z/3 have topological fundamental group Z/3. For this purpose, we describe degenerations to stable KSBA surfaces with one 1/4(1,1) singularity, whose minimal resolution are elliptic…

A new class of examples of surfaces with maximal Picard number is constructed. These carry pencils of genus two or three curves such their Jacobian fibrations are isogenous to fibre products of elliptic modular surfaces.

In this article we classify quadruple Galois canonical covers of smooth surfaces of minimal degree. The classification shows that they are either non-simple cyclic covers or bi-double covers. If they are bi-double then they are all fiber…

We compute equations for Coughlan's family of Godeaux surfaces with torsion $\mathbb Z/2$, which we call $\mathbb Z/2$-Godeaux surfaces, and we show that it is (at most) 7 dimensional. We classify non-rational KSBA degenerations $W$ of…

We fix some gaps of a proof of Xiao's conjecture on canonically fibered surfaces of relative genus 5 by the second author. Our argument simplifies the original proof and gives a much better bound on the geometric genus of the surface. Also…

A canonically fibered surface is a surface whose canonical series maps it to a curve. Using Miyaoka-Yau inequality, A. Beauville proved that a canonically fibered surface has relative genus at most 5 when its geometric genus is sufficiently…

Minimal algebraic surfaces of general type with the smallest possible invariants have geometric genus zero and K^2=1 and are usually called "numerical Godeaux surfaces". Although they have been studied by several authors, their complete…

We study the Hodge structure of elliptic surfaces which are canonically defined from bielliptic curves of genus three. We prove that the period map for the second cohomology has one dimensional fibers, and the period map for the total…

Motivated by a number of recent investigations, we define and investigate the various properties of the ruled surfaces depend on three dimensional Lie groups with a bi-variant metric. We give useful results involving the characterizations…

We give an algorithm to classify singular fibers of finite cyclic covering fibrations of a ruled surface by using singularity diagrams. As the first application, we classify all fibers of 3-cyclic covering fibrations of genus 4 of a ruled…

We construct some complex surfaces of general type with maximal Picard number. These examples arise as fibrations of genus two curves over quaternionic Shimura curves.

For a Riemannian submersion from a simple compact Lie group with a bi-invariant metric, we prove the action of its holonomy group on the fibers is transitive. As a step towards classifying Riemannian submersions with totally geodesic…

We complete the study of birational geometry of Fano fiber spaces $\pi\colon V\to {\mathbb P}^1$, the fiber of which is a Fano double hypersurface of index 1. For each family of these varieties we either prove birational rigidity or produce…

Motivated by a conjecture of Xiao, we study supporting divisors of fibred surfaces. On the one hand, after developing a formalism to treat one-dimensional families of varieties of any dimension, we give a structure theorem for fibred…

We produce a family of numerical Campedelli surfaces with \Z/6 torsion by constructing the (Gorenstein codimension 5) canonical ring of the \'{e}tale six to one cover using serial unprojection. In Section 2 we develop the necessary…

We study smooth bundles over surfaces with highly connected almost parallelizable fiber $M$ of even dimension, providing necessary conditions for a manifold to be bordant to the total space of such a bundle and showing that, in most cases,…