Stabilizers for nondegenerate matrices of boundary format and Steiner bundles

Carla Dionisi

paper

Stabilizers for nondegenerate matrices of boundary format and Steiner bundles

arXiv:math/0312264

Abstract

In this paper nondegenerate multidimensional matrices of boundary format in $V_{0} \otimes ... \otimes V_{p}$ are investigated by their link with Steiner vector bundles on product of projective spaces. For any nondegenerate matrix $A$ the stabilizer for the $S L (V_{0}) \times ... \times S L (V_{p})$ -action, $S t ab (A)$ , is completely described. In particular we prove that there exists an explicit action of SL(2) on $V_{0} \otimes ... \otimes V_{p}$ such that $S t ab (A)^{0} \subseteq S L (2)$ and the equality holds if and only if $A$ belongs to a unique $S L (V_{0}) \times > ... \times S L (V_{p})$ -orbit containing the identity matrices.

14 pages, Latex