Border Waring Rank via Asymptotic Rank

Abstract: We investigate an extension of a lower bound on the Waring (cactus) rank of homogeneous forms due to Ranestad and Schreyer. We show that for particular classes of homogeneous forms, for which a generalization of this method applies, the lower bound extends to the level of border (cactus) rank. The approach is based on recent results on tensor asymptotic rank.