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The genus of space curves

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Si dimostra che seC⊃ℙ 3 k (k di caratteristica qualunque) é una curva, non piana, localmente Cohen-Macaulay, di gradod, allorap a (C)≤((d−2)(d−3))/2. Si mostra che questa limitazione è ottimale, e si classificano le curve di genere aritmetico massimale.

Abstract

LetC be a curve contained in ℙ 3 k (k of any characteristic), which is locally Cohen-Macaulay, not contained in a plane and of degreed. We prove thatp a (C)≤≤((d−2)(d−3))/2. Moreover we show existence of curves with anyd, p a satisfying this inequality and we characterize those curves for which equality holds.

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  1. Robin Hartshorne

    Present address: Department of Mathematics, University of California, 94720, Berkeley, CA, USA

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    1. Robin Hartshorne
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    Hartshorne, R. The genus of space curves. Ann. Univ. Ferrara 40, 207–223 (1994). https://doi.org/10.1007/BF02834521

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