Tohoku Mathematical Journal

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

Hirotaka Ishida

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Abstract

In this paper, we study a minimal surface of general type with $p_g=q=1, K_S^2=3$ 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 $\Alb(S)\isom E$, 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 complex multiplication type.

Article information

Source
Tohoku Math. J. (2), Volume 58, Number 1 (2006), 33-69.

Dates
First available in Project Euclid: 18 April 2006

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1145390205

Digital Object Identifier
doi:10.2748/tmj/1145390205

Mathematical Reviews number (MathSciNet)
MR2221791

Zentralblatt MATH identifier
1112.14012

Subjects
Primary: 14D05: Structure of families (Picard-Lefschetz, monodromy, etc.)
Secondary: 14J29: Surfaces of general type 14D06: Fibrations, degenerations

Keywords
Surface of general type fibration of curves elliptic curve

Citation

Ishida, Hirotaka. Catanese-Ciliberto surfaces of fiber genus three with unique singular fiber. Tohoku Math. J. (2) 58 (2006), no. 1, 33--69. doi:10.2748/tmj/1145390205. https://projecteuclid.org/euclid.tmj/1145390205


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