# Duality of Multiple Root Loci

arXiv: https://arxiv.org/abs/1508.00202 · HTML: https://mlsanity.com/paper/1508.00202/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Aug 2015.

## Built on by (most cited first, 1 of 1)

- [Geometry of Linear Convolutional Networks](https://mlsanity.com/paper/2108.01538/) (2021)

## Abstract (arXiv)

The multiple root loci among univariate polynomials of degree n are indexed by partitions of n. We study these loci and their conormal varieties. The projectively dual varieties are joins of such loci where the partitions are hooks. Our emphasis lies on equations and parametrizations that are useful for Euclidean distance optimization. We compute the ED degrees for hooks. Among the dual hypersurfaces are those that demarcate the set of binary forms whose real rank equals the generic complex rank.