Algebra & Number Theory

Secant varieties of Segre–Veronese varieties

Claudiu Raicu

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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.

Article information

Algebra Number Theory, Volume 6, Number 8 (2012), 1817-1868.

Received: 30 June 2011
Revised: 15 December 2011
Accepted: 20 January 2012
First available in Project Euclid: 20 December 2017

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Zentralblatt MATH identifier

Primary: 14M17: Homogeneous spaces and generalizations [See also 32M10, 53C30, 57T15] 14M12: Determinantal varieties [See also 13C40]

Segre varieties Veronese varieties secant varieties


Raicu, Claudiu. Secant varieties of Segre–Veronese varieties. Algebra Number Theory 6 (2012), no. 8, 1817--1868. doi:10.2140/ant.2012.6.1817.

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