On quadratic generation of ideals defining projective toric varieties

For any ample line bundle L on a projective toric variety of dimension n, it is known that the line bundle L^⊗i is normally generated if i is greater than or equal to n - 1. We prove that L^⊗i is also normally presented if i is greater than or equal to n - 1. Furthermore we show that L^⊗i is normally presented for i ≥ [n/2] + 1 if L is normally generated.