Secant varieties of toric varieties arising from simplicial complexes

Motivated by the study of the secant variety of the Segre-Veronese variety we propose a general framework to analyze properties of the secant varieties of toric embeddings of affine spaces defined by simplicial complexes. We prove that every such secant is toric, which gives a way to use combinatori...

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Detalles Bibliográficos
Autores: Khadam, Muhammad Azeem, Michalek, Mateusz, Zwiernik, Piotr
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2020
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10230/46879
Acceso en línea:http://hdl.handle.net/10230/46879
http://dx.doi.org/10.1016/j.laa.2019.12.008
Access Level:acceso abierto
Palabra clave:Secant variety
Segre-Veronese embedding
Simplicial complex
Cumulants
Singular locus
Descripción
Sumario:Motivated by the study of the secant variety of the Segre-Veronese variety we propose a general framework to analyze properties of the secant varieties of toric embeddings of affine spaces defined by simplicial complexes. We prove that every such secant is toric, which gives a way to use combinatorial tools to study singularities. We focus on the Segre-Veronese variety for which we completely classify their secants that give Gorenstein or Q-Gorenstein varieties. We conclude providing the explicit description of the singular locus.