IJPAM: Volume 51, No. 3 (2009)

REDUCIBLE BIELLIPTIC CURVES

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: [email protected]


Abstract.Here we consider reducible bielliptic curves $u: X = X_1\cup X_2\to C$ with $C$ integral and $p_a(C)=1$. For certain bidegrees $(d_1,d_2)$ we prove the existence or non-existence of a finite morphism $f: X\to \mathbb {P}^1$ with bidegree $(d_1,d_2)$ such that the induced morphism $(u,f): X \to \mathbb {P}^1\times \mathbb {P}^1$ is birational onto its image.

Received: December 21, 2008

AMS Subject Classification: 14H20, 14H51

Key Words and Phrases: reducible curve, bielliptic curve

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 51
Issue: 3