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- W2889454921 abstract "Let $${P_{rm MAX}(d, s)}$$ denote the maximum arithmetic genus of a locally Cohen-Macaulay curve of degree d in $${mathbb{P}^3}$$ that is not contained in a surface of degree < s. A bound P(d, s) for $${P_{rm MAX}(d, s)}$$ has been proven by the first author in characteristic zero and then generalized in any characteristic by the third author. In this paper, we construct a large family $${mathcal{C}}$$ of primitive multiple lines and we conjecture that the generic element of $${mathcal{C}}$$ has good cohomological properties. From the conjecture it would follow that $${P(d, s) = P_{rm MAX}(d, s)}$$ for d = s and for every $${d geq 2s - 1}$$ . With the aid of Macaulay2 we checked this holds for $${s leq 120}$$ by verifying our conjecture in the corresponding range." @default.
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- W2889454921 date "2018-09-01" @default.
- W2889454921 modified "2023-10-16" @default.
- W2889454921 title "The Maximum Genus Problem for Locally Cohen-Macaulay Space Curves" @default.
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- W2889454921 doi "https://doi.org/10.1007/s00032-018-0284-2" @default.
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