We learned the following relationship between the degree and genus of plane curves in my algebraic geometry course:
\begin{array} a \text{degree} &d &1 &2 &3 &4 &5 &6 &7 & \dots\\ \text{genus} &g &0 &0 &1 &3 &6 &10 &15 & \dots \end{array}
So there are no plane curves of genus 2, 4, 5, etc. My question is: what is the relationship between degree and genus for space curves? In particular, do there also exists gaps like this? Why or why not?