The Maximum Genus Problem for Locally Cohen-Macaulay Space Curves

  title={The Maximum Genus Problem for Locally Cohen-Macaulay Space Curves},
  author={V. Beorchia and Paolo Lella and E. Schlesinger},
  journal={Milan Journal of Mathematics},
  • V. Beorchia, Paolo Lella, E. Schlesinger
  • Published 2018
  • Mathematics
  • Milan Journal of Mathematics
  • Let $${P_{\rm MAX}(d, s)}$$PMAX(d,s) denote the maximum arithmetic genus of a locally Cohen-Macaulay curve of degree d in $${\mathbb{P}^3}$$P3 that is not contained in a surface of degree < s. A bound P(d, s) for $${P_{\rm MAX}(d, s)}$$PMAX(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 $${\mathcal{C}}$$C of primitive multiple lines and we conjecture that the generic… CONTINUE READING
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