Four lectures on secant varieties

Abstract

This paper is based on the first author's lectures at the 2012 University of Regina Workshop "Connections Between Algebra and Geometry". Its aim is to provide an introduction to the theory of higher secant varieties and their applications. Several references and solved exercises are also included.

Lectures notes to appear in PROMS (Springer Proceedings in Mathematics & Statistics), Springer/Birkhauser

References in corpus (6)

• E-Determinants of Tensors
• Waring decompositions of monomials
• On the Waring problem for polynomial rings
• Symplectic bundles on the plane, secant varieties and Lüroth quartics revisited
• New lower bounds for the border rank of matrix multiplication
• Explicit tensors of border rank at least 2n-1

Cited by in corpus (11)

• The Hitchhiker guide to: Secant Varieties and Tensor Decomposition
• Equations for the fifth secant variety of Segre products of projective spaces
• Secant non-defectivity via collisions of fat points
• Border Ranks of Monomials
• Computations and Equations for Segre-Grassmann hypersurfaces
• Learning Algebraic Models of Quantum Entanglement
• Homotopy techniques for tensor decomposition and perfect identifiability
• Border Waring Rank via Asymptotic Rank
• The monic rank
• Waring decompositions of the product of two quadrics: the small rank cases
• The Waring rank of binary binomial forms