Syzygies, regularity and toric varieties
  Let A be an ample line bundle on a projective toric variety X of dimension n. We show that if l>=n-1+p, then A^l satisfies the property N_p. Applying similar methods, we obtain a combinatorial theorem: For a given lattice polytope P we give a criterion for an integer m to guarantee that mP is normal. 
Milena Hering