Comptes Rendus
no. 11
Combinatorics
Discriminantal arrangement, 3 × 3 minors of Plücker matrix and hypersurfaces in Grassmannian Gr(3,n)
[Arrangement discriminant, mineurs 3 × 3 de la matrice de Plücker et hypersurfaces de la grassmannienne Gr(3,n)]

Présenté par : the Editorial Board

Sumire Sawada1 ; Simona Settepanella1 ; So Yamagata1
1 Department of Mathematics, Hokkaido University, Japan
Comptes Rendus. Mathématique, Volume 355 (2017) no. 11, pp. 1111-1120.

We show that points in specific degree-2 hypersurfaces in the Grassmannian Gr(3,n) correspond to generic arrangements of n hyperplanes in C3 with associated discriminantal arrangement having intersections of multiplicity three in codimension two.

Nous montrons que les points d'hypersurfaces spécifiques de degré 2 de la grasmannienne Gr(3,n) correspondent aux arrrangements génériques de n hyperplans dans C3, dont l'arrangement discriminant possède des intersections de triplets d'hyperplans de codimension deux.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.10.011

Sumire Sawada 1 ; Simona Settepanella 1 ; So Yamagata 1

1 Department of Mathematics, Hokkaido University, Japan 
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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/

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  • Pragnya Das; Elisa Palezzato; Simona Settepanella The generalized Sylvester's and orchard problems via discriminantal arrangement, Innovations in Incidence Geometry, Volume 21 (2024) no. 1, pp. 117-130 | DOI:10.2140/iig.2024.21.117 | Zbl:1544.05022
  • So Yamagata A classification of combinatorial types of discriminantal arrangements, Journal of Algebraic Combinatorics, Volume 57 (2023) no. 4, pp. 1007-1032 | DOI:10.1007/s10801-022-01207-1 | Zbl:1516.52016
  • Simona Settepanella; So Yamagata On the non-very generic intersections in discriminantal arrangements, Comptes Rendus. Mathématique. Académie des Sciences, Paris, Volume 360 (2022), pp. 1027-1038 | DOI:10.5802/crmath.360 | Zbl:1498.52039
  • Beifang Chen; Houshan Fu; Suijie Wang Parallel translates of represented matroids, Advances in Applied Mathematics, Volume 127 (2021), p. 11 (Id/No 102176) | DOI:10.1016/j.aam.2021.102176 | Zbl:1462.52038
  • Takuro Abe; Alexandru Dimca; Eva-Maria Feichtner; Gerhard Röhrle Logarithmic vector fields and freeness of divisors and arrangements: new perspectives and applications. Abstracts from the workshop held January 24–30, 2021 (online meeting), Oberwolfach Rep. 18, No. 1, 225-300, 2021 | DOI:10.4171/owr/2021/5 | Zbl:1487.00025
  • Sumire Sawada; Simona Settepanella; So Yamagata Pappus's theorem in Grassmannian Gr(3,Cn), Ars Mathematica Contemporanea, Volume 16 (2019) no. 1, pp. 257-276 | DOI:10.26493/1855-3974.1619.a03 | Zbl:1420.52029

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