Asymptotic syzygies of algebraic varieties

Abstract

We study the asymptotic behavior of the syzygies of a smooth projective variety as the positivity of the embedding line bundle grows. The main result asserts that the syzygy modules are non-zero in almost all degrees allowed by Castelnuovo-Mumford regularity. We also give an effective statement for Veronese varieties that we conjecture to be optimal. © 2012 Springer-Verlag.