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...
| Autores: | , , |
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| 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 |
| 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. |
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