Hyperdeterminants of Polynomials

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 μ-discriminant of polynomial is found.

some typos corrected

References in corpus (1)

• E-Determinants of Tensors

Cited by in corpus (12)

• Four lectures on secant varieties
• Border Ranks of Monomials
• Computations and Equations for Segre-Grassmann hypersurfaces
• The 3 x 3 x 3 hyperdeterminant as a polynomial in the fundamental invariants for SL(3,C) x SL(3,C) x SL(3,C)
• Symmetrization of Principal Minors and Cycle-Sums
• Hyperdeterminants from the $E_8$ Discriminant
• On the algebraic boundaries among typical ranks for real binary forms
• On the product of the singular values of a binary tensor
• Multiplicities of eigenvalues of tensors
• Almost all subgeneric third-order Chow decompositions are identifiable
• Inverse tensor eigenvalue problem
• Binary forms of suprageneric rank and the multiple root loci