Real rank boundaries and loci of forms

2017/08/10 by Ventura, Emanuele
#14P10 #51N35 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1708.03078

Abstract

In this article we study forbidden loci and typical ranks of forms with respect to the embeddings of \mathbb P¹× \mathbb P¹ given by the line bundles (2,2d). We introduce the Ranestad-Schreyer locus corresponding to supports of non-reduced apolar schemes. We show that, in those cases, this is contained in the forbidden locus. Furthermore, for these embeddings, we give a component of the real rank boundary, the hypersurface dividing the minimal typical rank from higher ones. These results generalize to a class of embeddings of \mathbb Pⁿ× \mathbb P¹. Finally, in connection with real rank boundaries, we give a new interpretation of the 2× n × n hyperdeterminant.

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