Rate and syzygies of modules over Veronese subrings.

The rate of a graded moduleMover a standard graded algebraR,rateR(M), is a measure of the growth of the shifts in the minimal graded free resolution ofM. In this paper, we study the rate of Veronese modules ofM. More precisely, it is shown thatfor allc≥1. This extends a result of Aramova et al. [2] As a consequence of this, ifMis generated in degree zero, then, for allc≥max{rateR(M),Rate(R)}. Also, it is shown that, for all integerss,c≥1. In particular case, we give a simple proof to a result of Backelin. [ABSTRACT FROM PUBLISHER]