Catanese-Ciliberto surfaces of fiber genus three with unique singular fiber
Ishida, Hirotaka
Tohoku Math. J. (2), Tome 58 (2006) no. 1, p. 33-69 / Harvested from Project Euclid
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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.
Publié le : 2006-03-14
Classification:  Surface of general type,  fibration of curves,  elliptic curve,  14D05,  14J29,  14D06 
@article{1145390205,
     author = {Ishida, Hirotaka},
     title = {Catanese-Ciliberto surfaces of fiber genus three with unique singular fiber},
     journal = {Tohoku Math. J. (2)},
     volume = {58},
     number = {1},
     year = {2006},
     pages = { 33-69},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1145390205}
}

Ishida, Hirotaka. Catanese-Ciliberto surfaces of fiber genus three with unique singular fiber. Tohoku Math. J. (2), Tome 58 (2006) no. 1, pp.  33-69. http://gdmltest.u-ga.fr/item/1145390205/