Powers of ample divisors and syzygies of projective varieties

Original · EN

Suppose X is a projective variety, which needs not be smooth, and L an ample divisor on X. We show that there are integers c and b such that for any nonnegative integer p, Lᵈ is normally generated and embeds X as a variety who defining ideal has linear syzygies upto the p-th step (i.e. Lᵈ has property Nₚ) for all d >= cp + b.