# Catanese-Ciliberto surfaces of fiber genus three with unique singular fiber

@article{Ishida2006CataneseCilibertoSO, title={Catanese-Ciliberto surfaces of fiber genus three with unique singular fiber}, author={Hirotaka Ishida}, journal={Tohoku Mathematical Journal}, year={2006}, volume={58}, pages={33-69} }

In this paper, we study a minimal surface of general type with pg = q = 1, K2 S = 3 which we call a Catanese-Ciliberto surface. The Albanese map of this surface gives a fibration of curves over an elliptic curve. For an arbitrary elliptic curve E, we obtain the Catanese-Ciliberto surface which satisfies Alb(S) ∼= E, has no (−2)-curves and has a unique singular fiber. Furthermore, we show that the number of the isomorphism classes satisfying these conditions is four if E has no automorphism of…

## 12 Citations

THE MODULI SPACE OF CATANESE-CILIBERTO-ISHIDA SURFACES

- Mathematics
- 2013

We determine the moduli space of the surfaces of general type studied by Catanese, Ciliberto and Hirotaka Ishida by using the family of Hesse cubic curves. Introduction A minimal surfaceS of general…

Standard isotrivial fibrations with p_g=q=1, II

- Mathematics
- 2009

Abstract A smooth, projective surface S is called a standard isotrivial fibration if there exists a finite group G which acts faithfully on two smooth projective curves C and F so that S is…

The arithmetic and geometry of a class of algebraic surfaces of general type and geometric genus one

- Mathematics
- 2010

We study of a class of algebraic surfaces of general type and geometric genus one, with a view toward arithmetic results. These surfaces, called CC surfaces here, have been classified over the…

The Tate Conjecture for a family of surfaces of general type with pg = q = 1 and K2 = 3

- Mathematics
- 2015

We prove a big monodromy result for a smooth family of complex algebraic surfaces of general type, with invariants $p_g=q=1$ and $K^2=3$, that has been introduced by Catanese and Ciliberto. This is…

Kodaira fibrations and beyond: methods for moduli theory

- Mathematics
- 2015

Kodaira fibred surfaces are remarkable examples of projective classifying spaces, and there are still many intriguing open questions concerning them, especially the slope question. The topological…

Fibred algebraic surfaces and commutators in the Symplectic group

- Mathematics
- 2019

We describe the minimal number of critical points and the minimal number $s$ of singular fibres for a non isotrivial fibration of a surface $S$ over a curve $B$ of genus $1$, constructing a fibration…

LARGE MONODROMY FOR A FAMILY OF SURFACES OF GENERAL TYPE WITH

- 2009

We study a polarized family π : X → R of 2-dimensional complex projective varieties, originally constructed by Catanese and Ciliberto, whose smooth fibers are surfaces of general type with invariants…

Some results on surfaces with p_g=q=1 and K^2=2

- Mathematics
- 2015

Following an idea of Ishida, we develop polynomial equations for certain unramified double covers of surfaces with p_g=q=1 and K^2=2. Our first main result provides an explicit surface surface X with…

Bounds for the relative Euler-Poincaré characteristic of certain hyperelliptic fibrations

- Mathematics
- 2005

Abstract.In this paper, we find the lower bound for the relative Euler-Poincaré characteristic of a relatively minimal hyperelliptic fibration with slope four. We prove the existence of hyperelliptic…

Semistable fibrations over an elliptic curve with only one singular fibre

- Mathematics
- 2017

In this work we describe a construction of semistable fibrations over an elliptic curve with one unique singular fibre and we give effective examples using monodromy of curves.

## References

SHOWING 1-7 OF 7 REFERENCES

Vector Bundles Over an Elliptic Curve

- Mathematics
- 1957

Introduction THE primary purpose of this paper is the study of algebraic vector bundles over an elliptic curve (defined over an algebraically closed field k). The interest of the elliptic curve lies…

Vector bundles on an elliptic curve

- Mathematics
- 1971

Let k be an algebraically closed field of characteristic p≧ 0, and let X be an abelian variety over k. The goal of this paper is to answer the following questions, when dim(X) = 1 and p≠0, posed by…

Certain algebraic surfaces of general type with irregularity one and their canonical mappings

- Mathematics
- 1998

CILIBERTO, Symmetric products of ellipticcurves and surfaces of general type with pg = q = 1, J

- Algebraic Geom
- 1993

CILIBERTO, Surfaces with pg = q = 1, Problems inthe theory of surfaces and their classification (Cortona

- 1991