Toric degenerations of Grassmannians from matching fields
Algebraic Combinatorics, Volume 2 (2019) no. 6, pp. 1109-1124.

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).

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DOI: 10.5802/alco.77
Classification: 14M15,  14M25,  14T05
Keywords: toric degenerations, SAGBI and Khovanskii bases, Grassmannians, tropical geometry
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
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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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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