Spaces of Sums of Powers and Real Rank Boundaries
Mateusz Michałek and Hyunsuk Moon
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Submission date: 17. Jan. 2017 (revised version: January 2017)
Keywords and phrases: Real rank, tensors, VSP
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We investigate properties of Waring decompositions of real homogeneous forms. We study the moduli of real decompositions, so-called Space of Sums of Powers, naturally included in the Variety of Sums of Powers. Explicit results are obtained for quaternary quadrics, relating the algebraic boundary of SSP to various loci in the Hilbert scheme of four points in P^3. Further, we study the locus of general real forms whose real rank coincides with the complex rank. In case of quaternary quadrics the boundary of this locus is a degree forty hypersurface that is a join of the third secant variety and the tangential variety of the third veronese of P^3.