Comptes Rendus
Algebraic geometry
The boundary of the orbit of the 3-by-3 determinant polynomial
Comptes Rendus. Mathématique, Volume 354 (2016) no. 9, pp. 931-935.

We consider the 3×3 determinant polynomial and we describe the limit points of the set of all polynomials obtained from the determinant polynomial by linear change of variables. This answers a question of Joseph M. Landsberg.

Nous étudions le polynôme donné par le déterminant 3×3 et décrivons l'adhérence de l'ensemble des polynômes obtenus par changements de variables linéaires à partir de ce déterminant, ce qui répond à une question de Joseph M. Lansberg.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.07.002

Jesko Hüttenhain 1; Pierre Lairez 1

1 Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany
@article{CRMATH_2016__354_9_931_0,
     author = {Jesko H\"uttenhain and Pierre Lairez},
     title = {The boundary of the orbit of the 3-by-3 determinant polynomial},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {931--935},
     publisher = {Elsevier},
     volume = {354},
     number = {9},
     year = {2016},
     doi = {10.1016/j.crma.2016.07.002},
     language = {en},
}
TY  - JOUR
AU  - Jesko Hüttenhain
AU  - Pierre Lairez
TI  - The boundary of the orbit of the 3-by-3 determinant polynomial
JO  - Comptes Rendus. Mathématique
PY  - 2016
SP  - 931
EP  - 935
VL  - 354
IS  - 9
PB  - Elsevier
DO  - 10.1016/j.crma.2016.07.002
LA  - en
ID  - CRMATH_2016__354_9_931_0
ER  - 
%0 Journal Article
%A Jesko Hüttenhain
%A Pierre Lairez
%T The boundary of the orbit of the 3-by-3 determinant polynomial
%J Comptes Rendus. Mathématique
%D 2016
%P 931-935
%V 354
%N 9
%I Elsevier
%R 10.1016/j.crma.2016.07.002
%G en
%F CRMATH_2016__354_9_931_0
Jesko Hüttenhain; Pierre Lairez. The boundary of the orbit of the 3-by-3 determinant polynomial. Comptes Rendus. Mathématique, Volume 354 (2016) no. 9, pp. 931-935. doi : 10.1016/j.crma.2016.07.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.07.002/

[1] M.D. Atkinson Primitive spaces of matrices of bounded rank. II, J. Aust. Math. Soc. A, Volume 34 (1983) no. 3, pp. 306-315

[2] M. Bürgin; J. Draisma The Hilbert null-cone on tuples of matrices and bilinear forms, Math. Z., Volume 254 (2006) no. 4, pp. 785-809 | DOI

[3] J. Dieudonné Sur une généralisation du groupe orthogonal à quatre variables, Arch. Math., Volume 1 (1949), pp. 282-287 | DOI

[4] D. Eisenbud; J. Harris Vector spaces of matrices of low rank, Adv. Math., Volume 70 (1988) no. 2, pp. 135-155 | DOI

[5] D. Eisenbud; J. Harris The Geometry of Schemes, Grad. Texts Math., vol. 197, Springer-Verlag, New York, 2000 | DOI

[6] P. Fillmore; C. Laurie; H. Radjavi On matrix spaces with zero determinant, Linear Multilinear Algebra, Volume 18 (1985) no. 3, pp. 255-266 | DOI

[7] A. Grothendieck Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas, Publ. Math. IHÉS, Volume 32 (1967)

[8] J. Harris Algebraic Geometry. A First Course, Grad. Texts Math., vol. 133, Springer-Verlag, New York, 1995 (corrected reprint of the 1992 original)

[9] J. Landsberg; L. Manivel; N. Ressayre Hypersurfaces with degenerate duals and the geometric complexity theory program, Comment. Math. Helv., Volume 88 (2013) no. 2, pp. 469-484 | DOI

[10] J.M. Landsberg Geometric complexity theory: an introduction for geometers, Ann. Univ. Ferrara, Sez. 7: Sci. Mat., Volume 61 (2015) no. 1, pp. 65-117 | DOI

[11] K.D. Mulmuley; M. Sohoni Geometric complexity theory. I. An approach to the P vs. NP and related problems, SIAM J. Comput., Volume 31 (2001) no. 2, pp. 496-526 | DOI

[12] V.L. Popov; E.B. Vinberg Invariant theory (A.N. Parshin; I.R. Shafarevich, eds.), Algebraic Geometry IV, Encyclopaedia Math. Sci., vol. 55, Springer, Berlin, Heidelberg, 1994, pp. 123-278 | DOI

Cited by Sources:

Partially funded by the research grant BU 1371/2-2 of the Deutsche Forschungsgemeinschaft.

Comments - Policy