IJPAM: Volume 26, No. 2 (2006)

MULTIPLE COVERINGS OF CURVES
AND COHOMOLOGICAL INVARIANTS

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

Abstract.Let $f: X \to Y$ a degree covering between smooth and projective curves. Here (following [#!b!#]) we introduce some cohomological invariants of the rank vector bundle $f_\ast (\mathcal {O}_X)/\mathcal {O}_Y$ and give a condition which implies the existence of a smooth curve and morphisms $u: X \to Z$ , $v: Z \to Y$ such that $f = v\circ u$ and $1 < \deg (u) < k$ .