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# Terracini Loci and Homogeneous Spaces

## Terracini Loci et espaces homogènes

Edoardo Ballico
University of Trento
Italy

Published on 11 January 2021   DOI : 10.21494/ISTE.OP.2021.0760

### Mots-clés

We study the linear dependence of disjoint unions of double points of an integral and non-degenerate variety $X\subset ℙ^r$. Such sets are called Terracini loci. Our main results are for Segre-Veronese embeddings and a few other homogeneous spaces. To study the minimal number of such double points which are linearly dependent, it is useful to study the minimal degree curves contained in $X$. We give an example (the Segre embedding of ℙ1$\times$ ℙ1) in which these curves are not suffcient to describe these Terracini loci.

We study the linear dependence of disjoint unions of double points of an integral and non-degenerate variety $X\subset ℙ^r$. Such sets are called Terracini loci. Our main results are for Segre-Veronese embeddings and a few other homogeneous spaces. To study the minimal number of such double points which are linearly dependent, it is useful to study the minimal degree curves contained in $X$. We give an example (the Segre embedding of ℙ1$\times$ ℙ1) in which these curves are not suffcient to describe these Terracini loci.