Vol. 6, No. 8, 2012

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ISSN: 1944-7833 (e-only)
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Secant varieties of Segre–Veronese varieties

Claudiu Raicu

Vol. 6 (2012), No. 8, 1817–1868
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