Toward a Salmon Conjecture

DOI10.1080/10586458.2011.576539zbMath1262.14056arXiv1009.6181OpenAlexW2036933876WikidataQ123141605 ScholiaQ123141605MaRDI QIDQ4915397

Daniel J. Bates, Luke Oeding

Publication date: 10 April 2013

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1009.6181

zbMATH Keywords

Segre embeddingrepresentation theorynumerical algebraic geometrysecant varietiesborder rank

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Numerical computation of solutions to systems of equations (65H10) Representation theory for linear algebraic groups (20G05) Determinantal varieties (14M12) Group actions on varieties or schemes (quotients) (14L30) Vector and tensor algebra, theory of invariants (15A72) Actions of groups on commutative rings; invariant theory (13A50) Multilinear algebra, tensor calculus (15A69) Computational aspects in algebraic geometry (14Q99)

Related Items (17)

Local equations for equivariant evolutionary models ⋮ Equations for GL invariant families of polynomials ⋮ The quadrifocal variety ⋮ Abelian tensors ⋮ Developing a statistically powerful measure for quartet tree inference using phylogenetic identities and Markov invariants ⋮ Tensor decomposition and homotopy continuation ⋮ Ranks and symmetric ranks of cubic surfaces ⋮ Concise tensors of minimal border rank ⋮ Bounded-rank tensors are defined in bounded degree ⋮ Regenerative cascade homotopies for solving polynomial systems ⋮ Numerically deciding the arithmetically Cohen-Macaulayness of a projective scheme ⋮ Equations for Lower Bounds on Border Rank ⋮ A proof of the set-theoretic version of the salmon conjecture ⋮ Equations for the Fifth Secant Variety of Segre Products of Projective Spaces ⋮ Noetherian operators and primary decomposition ⋮ Homotopy techniques for tensor decomposition and perfect identifiability ⋮ Finiteness results for abelian tree models

Uses Software

• HOM4PS
• PHCpack
• SINGULAR
• LiE
• Bertini

Cites Work

• Equations for secant varieties of Veronese and other varieties
• Set-theoretic defining equations of the tangential variety of the Segre variety
• A proof of the set-theoretic version of the salmon conjecture
• HOM4PS-2.0: a software package for solving polynomial systems by the polyhedral homotopy continuation method
• Rank and optimal computation of generic tensors
• Phylogenetic invariants for the general Markov model of sequence mutation
• On the ideals of secant varieties of Segre varieties
• On the ideals of secant varieties to certain rational varieties
• Phylogenetic ideals and varieties for the general Markov model
• Regeneration homotopies for solving systems of polynomials
• Geometry and the complexity of matrix multiplication
• On the ideals and singularities of secant varieties of Segre varieties
• Induction for secant varieties of Segre varieties
• Adaptive Multiprecision Path Tracking
• Algorithm 795
• Prolongations and Computational Algebra
• Generalizations of Strassen's Equations for Secant Varieties of Segre Varieties

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