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 -planes in -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 -block diagonal, whose ideals are quadratically generated. These matching fields produce a new family of toric degenerations of .
Revised: 2019-03-04
Accepted: 2019-03-21
Published online: 2019-12-04
DOI: https://doi.org/10.5802/alco.77
Classification: 14M15, 14M25, 14T05
Keywords: toric degenerations, SAGBI and Khovanskii bases, Grassmannians, tropical geometry
@article{ALCO_2019__2_6_1109_0, 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}, doi = {10.5802/alco.77}, mrnumber = {4049839}, zbl = {07140426}, language = {en}, url = {https://alco.centre-mersenne.org/item/ALCO_2019__2_6_1109_0/} }
Mohammadi, Fatemeh; Shaw, Kristin. Toric degenerations of Grassmannians from matching fields. Algebraic Combinatorics, Volume 2 (2019) no. 6, pp. 1109-1124. doi : 10.5802/alco.77. https://alco.centre-mersenne.org/item/ALCO_2019__2_6_1109_0/
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