Set-theoretic defining equations of the tangential variety of the Segre variety

Abstract

We prove a set-theoretic version of the Landsberg--Weyman Conjecture on the defining equations of the tangential variety of a Segre product of projective spaces. We introduce and study the concept of exclusive rank. For the proof of this conjecture we use a connection to the author's previous work \cite{oeding_pm_paper, oeding_thesis} and re-express the tangential variety as the variety of principal minors of symmetric matrices that have exclusive rank no more than one.

13 pages

References in corpus (6)

• Eynard-Mehta theorem, Schur process, and their pfaffian analogs
• Hyperdeterminantal relations among symmetric principal minors
• Algebraic Factor Analysis: Tetrads, Pentads and Beyond
• Set Theoretic Defining Equations of the Variety of Principal Minors of Symmetric Matrices
• Secant Varieties of (P ^1) X .... X (P ^1) (n-times) are NOT Defective for n \geq 5
• On the ranks and border ranks of symmetric tensors

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• A Notable Relation between $N$-Qubit and $2^{N-1}$-Qubit Pauli Groups via Binary $\mathrm{LGr}(N,2N)$
• Symmetrization of Principal Minors and Cycle-Sums
• Lagrangian Grassmannians and Spinor Varieties in Characteristic Two
• Principal Minor Ideals and Rank Restrictions on their Vanishing Sets