## Algebra & Number Theory

### Secant varieties of Segre–Veronese varieties

Claudiu Raicu

#### Abstract

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

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

Dates
Revised: 15 December 2011
Accepted: 20 January 2012
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.ant/1513729916

Digital Object Identifier
doi:10.2140/ant.2012.6.1817

Mathematical Reviews number (MathSciNet)
MR3033528

Zentralblatt MATH identifier
1273.14102

#### Citation

Raicu, Claudiu. Secant varieties of Segre–Veronese varieties. Algebra Number Theory 6 (2012), no. 8, 1817--1868. doi:10.2140/ant.2012.6.1817. https://projecteuclid.org/euclid.ant/1513729916

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