# The Maximum Genus Problem for Locally Cohen-Macaulay Space Curves

@article{Beorchia2018TheMG,
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},
year={2018},
volume={86},
pages={137-155}
}
• 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
1 Citations
Stability and Applications
• Mathematics
• 2020
• 1
• PDF