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Toric degenerations of Grassmannians from matching fields. (English) Zbl 07140426
Summary: 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 \(\text{Gr}(3, n)\).

MSC:
14M15 Grassmannians, Schubert varieties, flag manifolds
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
14T05 Tropical geometry (MSC2010)
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