Secant varieties of Spinor varieties and of other generalized Grassmannians

Secant varieties are among the main protagonists in tensor decomposition, whose study involves both pure and applied mathematic areas. Despite they have been studied for decades, several aspects of their geometry are still mysterious, among which identifiability and singularity of their points. In this thesis we study the secant varieties of lines of Grassmannians and of Spinor varieties. As first result, we completely determine their posets of orbits under the action of the groups SL and Spin, respectively. Then we solve the problems of identifiability and tangential-identifiability of points in the secant varieties of lines: as a consequence, we also determine the second Terracini locus to a Grassmannian and to a Spinor variety. Our main result concerns the singular locus of the secant variety of lines: we completely determine it for Grassmannians, and we give lower and upper bounds for Spinor varieties. Finally, we partially describe the poset of orbits in the secant variety of lines of any cominuscule variety.

Grantor dc:publisher

Università degli studi di Trento

Year dc:date

2023

Author dc:creator

• Galgano, Vincenzo

Contributors dc:contributor

• Bernardi, Alessandra

• secant variety, Grassmannian, Spinor variety, homogeneous space, identifiability, tangential-identifiability, Terracini locus, singular locus.

Statement dc:rights

• info:eu-repo/semantics/openAccess
• license:Creative commons
• license uri:http://creativecommons.org/licenses/by-nd/4.0/

Language dc:language

eng

Identifier

http://dx.doi.org/10.15168/11572_398929
10.15168/11572_398929

OAI identifier oai:identifier

oai:iris.unitn.it:11572/398929