Binary forms of suprageneric rank and the multiple root loci

TL;DR

This paper explores the relationship between binary forms of a certain rank and the duals of multiple root loci, extending previous work and analyzing the structure and singularities of these varieties.

Contribution

It establishes a new connection between binary forms of suprageneric rank and dual multiple root loci, advancing understanding of their geometric properties.

Findings

Established the relation between binary forms of given rank and dual multiple root loci.

Described the stratification of these varieties.

Analyzed the singular loci of the varieties.

Abstract

We state the relation between the variety of binary forms of given rank and the dual of the multiple root loci. This is a new result for the suprageneric rank, as a continuation of the work by Buczy\'nski, Han, Mella and Teitler. We describe the strata of these varieties and explore their singular loci.