Standard Monomials and Gr\"obner Bases for Positroid Varieties

Author:

Ayah Almousa, Shiliang Gao, Daoji Huang

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Commutative Algebra (math.AC), Combinatorics (math.CO)

journal:

date:

2023-09-26 16:00:00

Abstract

We give an explicit characterization of the standard monomials of positroid varieties with respect to the Hodge degeneration, and give a Gr\"obner basis for positroid varieties. As an application, we show that promotion on rectangular-shaped semistandard tableaux gives a bijection between standard monomials of a positroid variety and its cyclic shifts.

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