Open Access
2006 Catanese-Ciliberto surfaces of fiber genus three with unique singular fiber
Hirotaka Ishida
Tohoku Math. J. (2) 58(1): 33-69 (2006). DOI: 10.2748/tmj/1145390205

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.

Citation

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Hirotaka Ishida. "Catanese-Ciliberto surfaces of fiber genus three with unique singular fiber." Tohoku Math. J. (2) 58 (1) 33 - 69, 2006. https://doi.org/10.2748/tmj/1145390205

Information

Published: 2006
First available in Project Euclid: 18 April 2006

zbMATH: 1112.14012
MathSciNet: MR2221791
Digital Object Identifier: 10.2748/tmj/1145390205

Subjects:
Primary: 14D05
Secondary: 14D06 , 14J29

Keywords: Elliptic curve , fibration of curves , Surface of general type

Rights: Copyright © 2006 Tohoku University

Vol.58 • No. 1 • 2006
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