On the third secant variety

Details On the third secant variety On the third secant variety

2011-11-29

arxiv.org/abs/1111.7005v1

Mathematics

Algebraic Geometry

21 pages

Scientific paper

We determine normal forms and ranks of tensors of border rank at most three. We present a differential-geometric analysis of limits of secant planes in a more general context. In particular there are at most four types of points on limiting trisecant planes for cominuscule varieties such as Grassmannians. We also show the singular locus of the first two secant varieties of all triple Segre products has codimension at least two.

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