Spaces of sums of powers and real rank boundaries

Michalek, Mateusz; Moon, Hyunsuk

doi:10.1007/s13366-018-0388-4

Spaces of sums of powers and real rank boundaries

Type of Publication:	Journal article
Publication status:	Published
URI (citable link):	http://nbn-resolving.de/urn:nbn:de:bsz:352-2-1ptl5x574jv2o9
Author:	Michalek, Mateusz; Moon, Hyunsuk
Year of publication:	2018
Published in:	Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry ; 59 (2018), 4. - pp. 645-663. - Springer. - ISSN 0138-4821. - eISSN 2191-0383
DOI (citable link):	https://dx.doi.org/10.1007/s13366-018-0388-4
Summary:	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 P³. Further, we study the locus of general real forms whose real rank coincides with the complex rank. In case of quaternary cubics the boundary of this locus is a degree forty hypersurface J(σ₃(v₃(P³)),τ(v₃(P³))).
Subject (DDC):	510 Mathematics
Keywords:	Space of sums of powers, Waring decomposition, Real rank, Variety of sums of powers
Link to License:	Attribution 4.0 International
Refereed:	Unknown

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MICHALEK, Mateusz, Hyunsuk MOON, 2018. Spaces of sums of powers and real rank boundaries. In: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry. Springer. 59(4), pp. 645-663. ISSN 0138-4821. eISSN 2191-0383. Available under: doi: 10.1007/s13366-018-0388-4

@article{Michalek2018-11Space-52472, title={Spaces of sums of powers and real rank boundaries}, year={2018}, doi={10.1007/s13366-018-0388-4}, number={4}, volume={59}, issn={0138-4821}, journal={Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry}, pages={645--663}, author={Michalek, Mateusz and Moon, Hyunsuk} }

2021-01-15T13:10:28Z 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 P3. Further, we study the locus of general real forms whose real rank coincides with the complex rank. In case of quaternary cubics the boundary of this locus is a degree forty hypersurface J(σ3(v3(P3)),τ(v3(P3))). 2021-01-15T13:10:28Z Michalek, Mateusz Attribution 4.0 International eng Moon, Hyunsuk Spaces of sums of powers and real rank boundaries Michalek, Mateusz 2018-11 Moon, Hyunsuk