Green's Conjecture for curves on rational surfaces with an anticanonical pencil

2012/07/30 by Margherita Lelli–Chiesa, Margherita Lelli-Chiesa, Lelli-Chiesa, Margherita
Mathematics · Social Sciences · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Historical and Political Studies #math.AG

paper · pdf · doi:10.48550/arxiv.1207.6993

Final version, to appear in Math. Zeit

openalex publication_date 2012/07/30 · arxiv created 2013/02/12 · arxiv updated 2013/02/13 · openalex created_date 2022/09/18 · openalex updated_date 2026/07/28

Abstract

Green's conjecture is proved for smooth curves C lying on a rational surface S with an anticanonical pencil, under some mild hypotheses on the line bundle L defined by C. Constancy of Clifford dimension, Clifford index and gonality of curves in the linear system |L| is also obtained.

Citations

• green's canonical syzygy conjecture for generic curves of odd genus

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