Algebraic boundaries among typical ranks for real binary forms of arbitrary degree

TL;DR

This paper investigates the algebraic boundaries of regions of real binary forms with fixed typical rank, revealing they are unions of dual varieties related to coincident root loci, thus advancing understanding of rank stratification.

Contribution

It establishes that the algebraic boundaries are unions of dual varieties to specific coincident root loci, providing a geometric characterization of typical rank boundaries.

Findings

Boundaries are unions of dual varieties to coincident root loci

Provides a geometric description of rank regions for real binary forms

Advances understanding of algebraic boundaries in tensor rank stratification

Abstract

We show that the algebraic boundaries of the regions of real binary forms with fixed typical rank are always unions of dual varieties to suitable coincident root loci.