On the algebraic boundaries among typical ranks for real binary forms

TL;DR

This paper characterizes the algebraic boundaries of regions of real binary forms with fixed typical rank up to degree eight, revealing their structure as dual varieties of specific coincident root loci.

Contribution

It identifies the algebraic boundaries of typical rank regions for real binary forms and relates them to dual varieties of coincident root loci, advancing understanding of rank stratification.

Findings

Boundaries are dual varieties of coincident root loci.

Results apply to binary forms of degree up to eight.

Provides a geometric description of rank regions.

Abstract

We describe the algebraic boundaries of the regions of real binary forms with fixed typical rank and of degree at most eight, showing that they are dual varieties of suitable coincident root loci.