Moves for Segre products Of Veronese subrings

We consider the Segre product of two square-free Veronese varietiesand we determine the set of moves associated to the correspondingsemigroup homomrphism. We define the initial vector of a generatormovie of the kernel of a semigroup homomorphism by the intialmonomial of the generator binomial of the toric ideal of the liftedalgebras homomorphism.