On Green and Green-Lazarfeld conjectures for simple coverings of algebraic curves

Details On Green and Green-Lazarfeld conjectures for simple coverings of algebraic curves On Green and Green-Lazarfeld conjectures for simple coverings of algebraic curves

2009-06-23

arxiv.org/abs/0906.4192v2

Mathematics

Algebraic Geometry

Added reference to a related previous result by Aprodu and Farkas kindly pointed out to the authors by an anonymous referee

Scientific paper

Let X be a smooth genus g curve equipped with a simple morphism f: X -> C, where C is either the projective line or more generally any smooth curve whose gonality is computed by finitely many pencils. Here we apply a method developed by Aprodu to prove that if g is big enough then X satisfies both Green and Green-Lazarsfeld conjectures. We also partially address the case in which the gonality of C is computed by infinitely many pencils.

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