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

2009/06/23 by Edoardo Ballico, Ballico, Edoardo, Claudio Fontanari +1
Computer Science · Mathematics · #14H51 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14H51

paper · pdf · doi:10.48550/arxiv.0906.4192

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

openalex publication_date 2009/06/23 · arxiv created 2009/09/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• On the projective normality of complete linear series on an algebraic curve
• green's canonical syzygy conjecture for generic curves of odd genus

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