Secant Varieties of Segre--Veronese Varieties

Details Secant Varieties of Segre--Veronese Varieties Secant Varieties of Segre--Veronese Varieties

2010-11-26

arxiv.org/abs/1011.5867v2

Mathematics

Algebraic Geometry

v2: this submission replaces the previous version, titled "The GSS conjecture", generalizing the results there to Segre--Veron

Scientific paper

We prove that the ideal of the variety of secant lines to a Segre--Veronese variety is generated in degree three by minors of flattenings. In the special case of a Segre variety this was conjectured by Garcia, Stillman and Sturmfels, inspired by work on algebraic statistics, as well as by Pachter and Sturmfels, inspired by work on phylogenetic inference. In addition, we describe the decomposition of the coordinate ring of the secant line variety of a Segre--Veronese variety into a sum of irreducible representations under the natural action of a product of general linear groups.

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