Asymptotic syzygies grow exponentially: a remark on a paper of   Ein-Lazarsfeld
  For all $2\leq q\leq \dim(X)$ and most relevant $p$ values, the dimension of the asymptotic Koszul cohomology group $K_{p,q}(X, B;L_d)$ grows exponentially with $d$. 
Daniel Chun and Ziv Ran
math.AG