Stabilizers for nondegenerate matrices of boundary format and Steiner bundles

Details Stabilizers for nondegenerate matrices of boundary format and Steiner bundles Stabilizers for nondegenerate matrices of boundary format and Steiner bundles

2003-12-12

arxiv.org/abs/math/0312264v2

Mathematics

Algebraic Geometry

14 pages, Latex

Scientific paper

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 $SL(V_0)\times ... \times SL(V_p)$-action, $Stab(A)$, 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 $Stab(A)^0\subseteq SL(2)$ and the equality holds if and only if $A$ belongs to a unique $SL(V_0)\times >... \times SL(V_p)$-orbit containing the identity matrices.

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