Abstract
In this paper we study graded Betti numbers of projective varieties. Using a spectral sequence argument, we establish an algebraic version of a duality Theorem proved first by Mark Green. Our approach doesn't require any smoothness or characteristic 0 assumption. We then study the graded Betti numbers of finite subschemes of a rational normal curve and apply these results to generalize another theorem of Mark Green, theK p.1 theorem, to some non-reduced schemes. Our result applies for instance in the case of ribbons.
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Supported by the Swiss National Research Fund
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Nagel, U., Pitteloud, Y. On graded Betti numbers and geometrical properties of projective varieties. Manuscripta Math 84, 291–314 (1994). https://doi.org/10.1007/BF02567458
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DOI: https://doi.org/10.1007/BF02567458