On the classification of non-aCM curves on quintic hypersurfaces in ℙ^3

02/08/2022

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by   Kenta Watanabe, et al.

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In this paper, we call a sub-scheme of dimension one in ℙ^3 a curve. It is well known that the arithmetic genus and the degree of an aCM curve D in ℙ^3 is computed by the h-vector of D. However, for a given curve D in ℙ^3, the two invariants of D do not tell us whether D is aCM or not. In this paper, we give a classification of curves on a smooth quintic hypersurface in ℙ^3 which are not aCM.