# 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…

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…

LARGE MONODROMY FOR A FAMILY OF SURFACES OF GENERAL TYPE WITH

- Mathematics
- 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.

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