Brill-Noether theory for cyclic covers

Abstract

The Brill-Noether Theorem gives necessary and sufficient conditions for the existence of a linear series. Here we consider a general n-fold, etale cyclic cover p of a curve C of genus g and investigate for which numbers r,d a linear series of dimension r and degree d exists on the covering curve. For r=1 this gives gonality. Using degeneration to a special singular example (containing a Castelnuovo canonical curve) and the theory of of limit linear series for tree-like curves we show that the Plücker formula yields a necessary condition for the existence of a linear series (of dimension r, degree d) which is only slightly weaker than the sufficient condition given by the result of Kleimann and Laksov, for all n,r,d.

References in corpus (1)

• Brill-Noether theory for cyclic covers

Cited by in corpus (5)

• Brill-Noether theory for cyclic covers
• Kirchhoff's theorem for Prym varieties
• On the Kodaira dimension of the moduli space of nodal curves
• Birational Geometry of moduli spaces of pointed curves
• The class of the Prym-Brill-Noether divisor