Abstract
Letρ C be the regularity of the Hilbert function of a projective curveC inP n K over an algebraically closed fieldK andβ 1,...,β n-1 be degrees for which there exists a complete intersection of type (β 1,...,β n-1) containing properlyC. Then the Castelnuovo-Mumford regularity ofC is bounded above by max {ρ C + 1,β 1 +...+β n-1-(n-1)}. We investigate the sharpness of the above bound, which is achieved by curves algebraically linked to ones having degenerate general hyperplane section.
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The authors were supported in part by MURST and GNSAGA.
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Cioffi, F., Marinari, M.G. & Ramella, L. Regularity bounds by minimal generators and Hilbert function. Collect. Math. 60, 89–100 (2009). https://doi.org/10.1007/BF03191218
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DOI: https://doi.org/10.1007/BF03191218