On quadratic generation of ideals defining projective toric varieties

Abstract

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.