TL;DR
This paper investigates the real rank two locus of algebraic varieties, providing a semi-algebraic description and characterizing tensors of real rank two, with focus on Segre and Veronese varieties.
Contribution
It offers a new semi-algebraic description of the real rank two locus and characterizes tensors of real rank two for Segre and Veronese varieties.
Findings
The algebraic boundary includes the tangential and edge varieties.
Provides a characterization of tensors with real rank two.
Describes the semi-algebraic structure of the real rank two locus.
Abstract
The real rank two locus of an algebraic variety is the closure of the union of all secant lines spanned by real points. We seek a semi-algebraic description of this set. Its algebraic boundary consists of the tangential variety and the edge variety. Our study of Segre and Veronese varieties yields a characterization of tensors of real rank two.
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