Stabilizers for nondegenerate matrices of boundary format and Steiner bundles.

Carla Dionisi

Revista Matemática Complutense (2004)

  • Volume: 17, Issue: 2, page 459-469
  • ISSN: 1139-1138

Abstract

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In this paper nondegenerate multidimensional matrices of boundary format in V0 ⊗ ... ⊗ Vp are investigated by their link with Steiner vector bundles on product of projective spaces. For any nondegenerate matrix A the stabilizer for the SL(V0) x ... x SL(Vp)-action, Stab(A), is completely described. In particular we prove that there exists an explicit action of SL(2) on V0 ⊗ ... ⊗ Vp such that Stab(A)0 ⊆ SL(2) and the equality holds if and only if A belongs to a unique SL(V0) x ... x SL(Vp)-orbit containing the identity matrices, according to [1].

How to cite

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Dionisi, Carla. "Stabilizers for nondegenerate matrices of boundary format and Steiner bundles.." Revista Matemática Complutense 17.2 (2004): 459-469. <http://eudml.org/doc/44448>.

@article{Dionisi2004,
abstract = {In this paper nondegenerate multidimensional matrices of boundary format in V0 ⊗ ... ⊗ Vp are investigated by their link with Steiner vector bundles on product of projective spaces. For any nondegenerate matrix A the stabilizer for the SL(V0) x ... x SL(Vp)-action, Stab(A), is completely described. In particular we prove that there exists an explicit action of SL(2) on V0 ⊗ ... ⊗ Vp such that Stab(A)0 ⊆ SL(2) and the equality holds if and only if A belongs to a unique SL(V0) x ... x SL(Vp)-orbit containing the identity matrices, according to [1].},
author = {Dionisi, Carla},
journal = {Revista Matemática Complutense},
keywords = {Espacios y haces de fibras; Teoría de matrices; Hipersuperficies; Invariantes; Haces vectoriales; vector bundles; multidimensional matrices; theory of invariants},
language = {eng},
number = {2},
pages = {459-469},
title = {Stabilizers for nondegenerate matrices of boundary format and Steiner bundles.},
url = {http://eudml.org/doc/44448},
volume = {17},
year = {2004},
}

TY - JOUR
AU - Dionisi, Carla
TI - Stabilizers for nondegenerate matrices of boundary format and Steiner bundles.
JO - Revista Matemática Complutense
PY - 2004
VL - 17
IS - 2
SP - 459
EP - 469
AB - In this paper nondegenerate multidimensional matrices of boundary format in V0 ⊗ ... ⊗ Vp are investigated by their link with Steiner vector bundles on product of projective spaces. For any nondegenerate matrix A the stabilizer for the SL(V0) x ... x SL(Vp)-action, Stab(A), is completely described. In particular we prove that there exists an explicit action of SL(2) on V0 ⊗ ... ⊗ Vp such that Stab(A)0 ⊆ SL(2) and the equality holds if and only if A belongs to a unique SL(V0) x ... x SL(Vp)-orbit containing the identity matrices, according to [1].
LA - eng
KW - Espacios y haces de fibras; Teoría de matrices; Hipersuperficies; Invariantes; Haces vectoriales; vector bundles; multidimensional matrices; theory of invariants
UR - http://eudml.org/doc/44448
ER -

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