The maximal genus of space curves in the range A

Edoardo Ballico; Philippe Ellia

The maximal genus of space curves in the range A

Algebraic Geometry 2020-10-28 v2

Authors: Edoardo Ballico , Philippe Ellia

Abstract

Fix positive integers d;m such that $(m^2+4m+6)/6 \leq d < (m^2+4m+6)/3$ (the so-called Range A for space curves). Let G(d;m) be the maximal genus of a smooth and connected curve, of degree d, $C \subset P^3$ such that $h^0(I_C(m-1)) = 0$ . Here we prove that $G(d,m) = 1+(m-1)d -\binom{m+2}{3}$ if $m\ge 13.8\cdot 10^5$ .

Keywords

space curves maximal genus range a postulation projective space smooth connected curve

Cite

@article{arxiv.1811.08807,
  title  = {The maximal genus of space curves in the range A},
  author = {Edoardo Ballico and Philippe Ellia},
  journal= {arXiv preprint arXiv:1811.08807},
  year   = {2020}
}

Comments

Some minor changes

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