Secant varieties of Segre–Veronese varieties

Raicu, Claudiu

doi:10.2140/ant.2012.6.1817

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Secant varieties of Segre–Veronese varieties

Claudiu Raicu

Vol. 6 (2012), No. 8, 1817–1868

DOI: 10.2140/ant.2012.6.1817

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.

Keywords

Segre varieties, Veronese varieties, secant varieties

Mathematical Subject Classification 2010

Primary: 14M17, 14M12

Milestones

Received: 30 June 2011

Revised: 15 December 2011

Accepted: 20 January 2012

Published: 14 December 2012

Authors

Claudiu Raicu
Department of Mathematics Princeton University Fine Hall, Washington Road Princeton, NJ 08544-1000 United States	Institute of Mathematics “Simion Stoilow” Romanian Academy of Sciences 21 Calea Grivitei Street 010702 Bucharest Romania

Vol. 6, No. 8, 2012