The maximal genus of space curves in the range A

Abstract

Fix positive integers d;m such that $(m^2+4m+6)/6\le d<(m^2+4m+6)/3$ (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 $G(d,m)=1+(m-1)d-\left(\genfrac{}{}{0ex}{}{m+2}{3}\right)$ if $m\ge 13.8\cdot 10^5$.

Some minor changes