Legendrian curves in $\mathbb C P^3$: cubics and curves on a quadric   surface
  We prove that the number of legendrian rational cubics in $\mathbb C P^3$ through three generic points and a line is three; also we classify all legendrian curves on a quadric surface. Several computations are additionally verified using Macaulay2 computer algebra system. 
Nikita Kalinin
math.AG