Stability of syzygy bundles on an algebraic surface
  Given a very ample line bundle L on a projective variety X, the syzygy bundle M_L associated to L is the kernel of the evaluation map on sections of L. Our main result is that if X is a smooth projective surface defined over an algebraically closed field, then M_L is slope-stable for any sufficiently positive L. 
Lawrence Ein, Robert Lazarsfeld, Yusuf Mustopa
math.AG