Toric degenerations of Grassmannians from matching fields

Mohammadi, Fatemeh; Shaw, Kristin

doi:10.5802/alco.77

Mohammadi, Fatemeh ¹ ; Shaw, Kristin ²

¹ University of Bristol Bristol BS8 1TW, UK
² University of Oslo P.O. box 1053 Blindern 0316 OSLO, Norway

Algebraic Combinatorics, Tome 2 (2019) no. 6, pp. 1109-1124.

Résumé

We study the algebraic combinatorics of monomial degenerations of Plücker forms which is governed by matching fields in the sense of Sturmfels and Zelevinsky. We provide a necessary condition for a matching field to yield a SAGBI basis of the Plücker algebra for $3$ -planes in $n$ -space. When the ideal associated to the matching field is quadratically generated this condition is both necessary and sufficient. Finally, we describe a family of matching fields, called $2$ -block diagonal, whose ideals are quadratically generated. These matching fields produce a new family of toric degenerations of $Gr (3, n)$ .

Reçu le : 2018-09-18
Révisé le : 2019-03-04
Accepté le : 2019-03-21
Publié le : 2019-12-04

MR Zbl

DOI : 10.5802/alco.77

Classification : 14M15, 14M25, 14T05
Mots-clés : toric degenerations, SAGBI and Khovanskii bases, Grassmannians, tropical geometry

Affiliations des auteurs :

Mohammadi, Fatemeh ¹ ; Shaw, Kristin ²

¹ University of Bristol Bristol BS8 1TW, UK
² University of Oslo P.O. box 1053 Blindern 0316 OSLO, Norway

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     author = {Mohammadi, Fatemeh and Shaw, Kristin},
     title = {Toric degenerations of {Grassmannians} from matching fields},
     journal = {Algebraic Combinatorics},
     pages = {1109--1124},
     publisher = {MathOA foundation},
     volume = {2},
     number = {6},
     year = {2019},
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     mrnumber = {4049839},
     zbl = {07140426},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/alco.77/}
}

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Mohammadi, Fatemeh; Shaw, Kristin. Toric degenerations of Grassmannians from matching fields. Algebraic Combinatorics, Tome 2 (2019) no. 6, pp. 1109-1124. doi : 10.5802/alco.77. http://www.numdam.org/articles/10.5802/alco.77/

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