On generators of ideals defining projective toric varieties

For any ample line bundle L on a projective toric variety of dimension n, it is proved that the line bundle L-circle timesi is normally generated if i is greater than or equal to n - 1, and examples showing that this estimate is best possible are given. Moreover we prove an estimate for the degree of the generators of the ideals defining projective toric varieties. In particular, when L is normally generated, the defining ideal of the variety embedded by the global sections of L has generators of degree at most n + 1. When the variety is embedded by the global sections of Lcircle times(n -1), then the defining ideal has generators of degree at most three.