Commutative Algebra and Algebraic Geometry: Real Rank Two Geometry

Seminar | February 14 | 5-6 p.m. | 939 Evans Hall

 Anna Seigal, UC Berkeley

 Department of Mathematics

A tensor is real rank two if it can be written as a sum of two real outer products of vectors. Similarly, the real rank two locus of an algebraic variety is the union of all secant lines spanned by real points. We seek a semi-algebraic description of this set and its boundary. Our study of Segre and Veronese varieties yields a characterization of tensors of real rank two. We also examine the real rank two locus of a curve in three-dimensional space. This talk is based on joint work with Bernd Sturmfels.