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$% C. Dionisi, Stabilizers for nondegenerate matrices of boundary format and Steiner
bundles, Rev. Mat. Complut. 17 (2004), 459–469.%$
Stabilizers for Nondegenerate Matrices of
Boundary Format and Steiner Bundles
Carla DIONISI
Dipartimento di Matematica Applicata “G. Sansone”
Via S. Marta, 3
I-50139, Firenze — Italy
Received:
February 25, 2002
Accepted: April 26, 2004
ABSTRACT
In this paper nondegenerate multidimensional matrices of boundary format in
are investigated by their link with Steiner vector bundles on
product of projective spaces. For any nondegenerate matrix
the stabilizer
for the
-action,
, is completely described.
In particular we prove that there exists an explicit action of
on
such that
and the equality holds if and only
if
belongs to a unique
-orbit containing the identity
matrices, according to Ancona and Ottaviani (2001).
Key words: vector bundles, multidimensional matrices, theory of invariants.
2000 Mathematics Subject Classification: 14F05, 15A72.