Identifiability and singular locus of secant varieties to Grassmannians

Fuente: arXiv
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Main Authors: Galgano, Vincenzo, Staffolani, Reynaldo
Format: Preprint
Published: 2022
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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
id 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