Hyperdeterminants of Polynomials

TL;DR

This paper explores the structure of hyperdeterminants of polynomials viewed as symmetric tensors, identifying their irreducible factors, degrees, and multiplicities using geometric methods.

Contribution

It provides a detailed geometric analysis of hyperdeterminants and -discriminants, revealing their factorization and multiplicity structure.

Findings

Hyperdeterminants factor into irreducible components with specific multiplicities.

The degrees of these factors are explicitly determined.

An analogous decomposition for the -discriminant is established.

Abstract

The hyperdeterminant of a polynomial (interpreted as a symmetric tensor) factors into several irreducible factors with multiplicities. Using geometric techniques these factors are identified along with their degrees and their multiplicities. The analogous decomposition for the \mu-discriminant of polynomial is found.