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We have decided to discontinue the publication of preprints on our preprint server end of 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
Spaces of Sums of Powers and Real Rank Boundaries
Mateusz Michałek and Hyunsuk MoonAbstract
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.
- Received:
- 17.01.17
- Published:
- 13.02.17
- Keywords:
- Real rank, tensors, VSP