Collineation varieties of tensors
Abstract In this article, we introduce the k -th collineation variety of a third order tensor. This is the closure of the image of the rational map of size k minors of a matrix of linear forms associated to the tensor. We classify such varieties in the case of pencils of matrices, and nets of matrices of small size. We discuss the natural stratification of tensor spaces induced by the invariants and the geometric type of the collineation varieties.
Authors
- Hanieh Keneshlou
- Fulvio Gesmundo (ORCID: https://orcid.org/0000-0001-6402-021X)
Institutions
- Centre National de la Recherche Scientifique (FR)
- Université Toulouse III - Paul Sabatier (FR)
- Université Fédérale de Toulouse Midi-Pyrénées (FR)
- University of Konstanz (DE)
- Toulouse Mathematics Institute (FR)
Publication Details
- Journal
- Collectanea mathematica
- Published
- 2025-01-22
- DOI
- https://doi.org/10.1007/s13348-025-00467-x
- Primary Topic
- Tensor decomposition and applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Deutsche Forschungsgemeinschaft