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 .
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Accepted:
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DOI: 10.5802/alco.77
Keywords: toric degenerations, SAGBI and Khovanskii bases, Grassmannians, tropical geometry
Mohammadi, Fatemeh 1; Shaw, Kristin 2
@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}, zbl = {07140426}, mrnumber = {4049839}, language = {en}, url = {https://alco.centre-mersenne.org/articles/10.5802/alco.77/} }
TY - JOUR AU - Mohammadi, Fatemeh AU - Shaw, Kristin TI - Toric degenerations of Grassmannians from matching fields JO - Algebraic Combinatorics PY - 2019 SP - 1109 EP - 1124 VL - 2 IS - 6 PB - MathOA foundation UR - https://alco.centre-mersenne.org/articles/10.5802/alco.77/ DO - 10.5802/alco.77 LA - en ID - ALCO_2019__2_6_1109_0 ER -
%0 Journal Article %A Mohammadi, Fatemeh %A Shaw, Kristin %T Toric degenerations of Grassmannians from matching fields %J Algebraic Combinatorics %D 2019 %P 1109-1124 %V 2 %N 6 %I MathOA foundation %U https://alco.centre-mersenne.org/articles/10.5802/alco.77/ %R 10.5802/alco.77 %G en %F 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/articles/10.5802/alco.77/
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