[Arrangement discriminant, mineurs 3 × 3 de la matrice de Plücker et hypersurfaces de la grassmannienne Gr(3,n)]
Nous montrons que les points d'hypersurfaces spécifiques de degré 2 de la grasmannienne correspondent aux arrrangements génériques de n hyperplans dans , dont l'arrangement discriminant possède des intersections de triplets d'hyperplans de codimension deux.
We show that points in specific degree-2 hypersurfaces in the Grassmannian correspond to generic arrangements of n hyperplanes in with associated discriminantal arrangement having intersections of multiplicity three in codimension two.
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@article{CRMATH_2017__355_11_1111_0,
author = {Sumire Sawada and Simona Settepanella and So Yamagata},
title = {Discriminantal arrangement, 3\,{\texttimes}\,3 minors of {Pl\"ucker} matrix and hypersurfaces in {Grassmannian} {\protect\emph{Gr}(3,\protect\emph{n})}},
journal = {Comptes Rendus. Math\'ematique},
pages = {1111--1120},
publisher = {Elsevier},
volume = {355},
number = {11},
year = {2017},
doi = {10.1016/j.crma.2017.10.011},
language = {en},
}
TY - JOUR AU - Sumire Sawada AU - Simona Settepanella AU - So Yamagata TI - Discriminantal arrangement, 3 × 3 minors of Plücker matrix and hypersurfaces in Grassmannian Gr(3,n) JO - Comptes Rendus. Mathématique PY - 2017 SP - 1111 EP - 1120 VL - 355 IS - 11 PB - Elsevier DO - 10.1016/j.crma.2017.10.011 LA - en ID - CRMATH_2017__355_11_1111_0 ER -
%0 Journal Article %A Sumire Sawada %A Simona Settepanella %A So Yamagata %T Discriminantal arrangement, 3 × 3 minors of Plücker matrix and hypersurfaces in Grassmannian Gr(3,n) %J Comptes Rendus. Mathématique %D 2017 %P 1111-1120 %V 355 %N 11 %I Elsevier %R 10.1016/j.crma.2017.10.011 %G en %F CRMATH_2017__355_11_1111_0
Sumire Sawada; Simona Settepanella; So Yamagata. Discriminantal arrangement, 3 × 3 minors of Plücker matrix and hypersurfaces in Grassmannian Gr(3,n). Comptes Rendus. Mathématique, Volume 355 (2017) no. 11, pp. 1111-1120. doi : 10.1016/j.crma.2017.10.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.10.011/
[1] The largest intersection lattice of a discriminantal arrangement, Beitr. Algebra Geom., Volume 40 (1999) no. 2, pp. 283-289
[2] Adjoints of oriented matroids, Combinatorica, Volume 6 (1986), pp. 299-308
[3] Discriminantal arrangements, fiber polytopes and formality, J. Algebraic Comb., Volume 6 (1997), pp. 229-246
[4] Concurrence geometries, Adv. Math., Volume 54 (1984) no. 3, pp. 278-301
[5] A note on discriminantal arrangements, Proc. Amer. Math. Soc., Volume 122 (1994) no. 4, pp. 1221-1227
[6] Algebraic Geometry: A First Course, Springer-Verlag, 1992
[7] Braided monoidal 2-categories and Manin–Schechtman higher braid groups, J. Pure Appl. Algebra, Volume 92 (1994) no. 3, pp. 241-267
[8] A presentation for Manin and Schechtman's higher braid groups, 1991 http://www.ma.huji.ac.il/~ruthel/papers/premsh.html (MSRI pre-print)
[9] Strata of discriminantal arrangements | arXiv
[10] Arrangements of hyperplanes, higher braid groups and higher Bruhat orders, Algebraic Number Theory in Honor K. Iwasawa, Advanced Studies in Pure Mathematics, vol. 17, 1989, pp. 289-308
[11] Introduction to Arrangements, CBMS Reg. Conf. Ser. Math., vol. 72, American Mathematical Society, Providence, RI, USA, 1989
[12] Arrangements of Hyperplanes, Grundlehren der Mathematischen Wissenschaften, Fundamental Principles of Mathematical Sciences, vol. 300, Springer-Verlag, Berlin, 1992
[13] Divisorial cohomology vanishing on toric varieties, Doc. Math., Volume 16 (2011), pp. 209-251
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On the non-very generic intersections in discriminantal arrangements
Simona Settepanella; So Yamagata
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