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

  title={Catanese-Ciliberto surfaces of fiber genus three with unique singular fiber},
  author={Hirotaka Ishida},
  journal={Tohoku Mathematical Journal},
  • H. Ishida
  • Published 30 March 2006
  • Mathematics
  • Tohoku Mathematical Journal
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… 

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