GdT Géométrie Algébrique Complexe

Collineation varieties of tensors

by Fulvio Gesmundo

Salle Picard

Salle Picard


A linear space of matrices gives rise naturally to a family of algebraic varieties: the k-th collineation variety arises from the parametrization induced by the minors of size k. We propose the study of collineation varieties to obtain `equations' for interesting varieties in the space of tensors. In particular, I will show to what extent the collineation varieties, and their geometric invariants (e.g. their degree) separate orbit-closures in the case of tensors of small dimension. This is part of joint work with Hanieh Keneshlou.