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arxiv: 1207.6993 · v2 · pith:RXCOIWS2new · submitted 2012-07-30 · 🧮 math.AG

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

classification 🧮 math.AG
keywords curvesanticanonicalcliffordconjecturegreenpencilrationalbundle
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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.

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