Identifiability and singular locus of secant varieties to Grassmannians
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866914631223607296 |
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| author | Galgano, Vincenzo Staffolani, Reynaldo |
| author_facet | Galgano, Vincenzo Staffolani, Reynaldo |
| contents | Secant varieties are among the main protagonists in tensor decomposition, whose study involves both pure and applied mathematical areas. Grassmannians are the building blocks for skewsymmetric tensors. Although they are ubiquitous in the literature, the geometry of their secant varieties is not completely understood. In this work we determine the singular locus of the secant variety of lines to a Grassmannian Gr(k,V) using its structure as SL(V)-variety. We solve the problems of identifiability and tangential-identifiability of points in the secant variety: as a consequence, we also determine the second Terracini locus to a Grassmannian. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2212_05811 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Identifiability and singular locus of secant varieties to Grassmannians Galgano, Vincenzo Staffolani, Reynaldo Algebraic Geometry 14M15, 14M17, 14N07 Secant varieties are among the main protagonists in tensor decomposition, whose study involves both pure and applied mathematical areas. Grassmannians are the building blocks for skewsymmetric tensors. Although they are ubiquitous in the literature, the geometry of their secant varieties is not completely understood. In this work we determine the singular locus of the secant variety of lines to a Grassmannian Gr(k,V) using its structure as SL(V)-variety. We solve the problems of identifiability and tangential-identifiability of points in the secant variety: as a consequence, we also determine the second Terracini locus to a Grassmannian. |
| title | Identifiability and singular locus of secant varieties to Grassmannians |
| topic | Algebraic Geometry 14M15, 14M17, 14N07 |
| url | https://arxiv.org/abs/2212.05811 |