Geodesic
Semi-inverted linear spaces and an analogue of the broken circuit complex
Scholten, Georgy1 ; Vinzant, Cynthia1
1 North Carolina State University Dept. of Mathematics Raleigh NC 27695, USA
Algebraic Combinatorics, Tome 2 (2019) no. 4, pp. 645-661

Voir la notice de l'article provenant de la source Numdam

The image of a linear space under inversion of some coordinates is an affine variety whose structure is governed by an underlying hyperplane arrangement. In this paper, we generalize work by Proudfoot and Speyer to show that circuit polynomials form a universal Gröbner basis for the ideal of polynomials vanishing on this variety. The proof relies on degenerations to the Stanley–Reisner ideal of a simplicial complex determined by the underlying matroid, which is closely related to the external activity complex defined by Ardila and Boocher. If the linear space is real, then the semi-inverted linear space is also an example of a hyperbolic variety, meaning that all of its intersection points with a large family of linear spaces are real.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/alco.65
Keywords: Matroid, hyperplane arrangement, simplicial complex, reciprocal linear space

Scholten, Georgy 1 ; Vinzant, Cynthia 1

1 North Carolina State University Dept. of Mathematics Raleigh NC 27695, USA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
@article{ALCO_2019__2_4_645_0,
     author = {Scholten, Georgy and Vinzant, Cynthia},
     title = {Semi-inverted linear spaces and an analogue of the broken circuit complex},
     journal = {Algebraic Combinatorics},
     pages = {645--661},
     publisher = {MathOA foundation},
     volume = {2},
     number = {4},
     year = {2019},
     doi = {10.5802/alco.65},
     mrnumber = {3997516},
     zbl = {1417.05254},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5802/alco.65/}
}
TY  - JOUR
AU  - Scholten, Georgy
AU  - Vinzant, Cynthia
TI  - Semi-inverted linear spaces and an analogue of the broken circuit complex
JO  - Algebraic Combinatorics
PY  - 2019
SP  - 645
EP  - 661
VL  - 2
IS  - 4
PB  - MathOA foundation
UR  - http://geodesic.mathdoc.fr/articles/10.5802/alco.65/
DO  - 10.5802/alco.65
LA  - en
ID  - ALCO_2019__2_4_645_0
ER  - 
%0 Journal Article
%A Scholten, Georgy
%A Vinzant, Cynthia
%T Semi-inverted linear spaces and an analogue of the broken circuit complex
%J Algebraic Combinatorics
%D 2019
%P 645-661
%V 2
%N 4
%I MathOA foundation
%U http://geodesic.mathdoc.fr/articles/10.5802/alco.65/
%R 10.5802/alco.65
%G en
%F ALCO_2019__2_4_645_0
Scholten, Georgy; Vinzant, Cynthia. Semi-inverted linear spaces and an analogue of the broken circuit complex. Algebraic Combinatorics, Tome 2 (2019) no. 4, pp. 645-661. doi: 10.5802/alco.65

Cité par Sources :