# IJPAM: Volume 26, No. 3 (2006)

SMOOTH CURVES COVERING TWO CURVES
OF POSITIVE GENUS

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it

Abstract.Fix integers , , , , , , . Set and define by decreasing induction the integers , by the formula . Fix smooth and connected projective curves , , such that and there is , , spanned by its global sections. Set and . Assume and for . Here we prove the existence of a smooth and connected genus projective curve and degree morphisms , , such that , , and all morphisms , , are birational onto its image.