Elimination ideals of Pl\"ucker ideals and algebras with straightening laws
Viktoriia Borovik, Takayuki Hibi

TL;DR
This paper investigates the algebraic structure of the Grassmannian's Pl"ucker ideal, focusing on quadratic relations, and characterizes certain Gorenstein subalgebras with straightening laws.
Contribution
It provides a combinatorial characterization of Gorenstein ASL subalgebras within the Pl"ucker algebra of Grassmannians of lines.
Findings
Quadratic Pl"ucker relations form a Gr"obner basis.
Identification of Gorenstein ASL subalgebras.
Characterization of projections of the Grassmannian of lines.
Abstract
It is well known that the Pl\"ucker ideal defining the Grassmannian is generated by quadratic Pl\"ucker relations. These relations form a reverse lexicographic Gr\"obner basis and endow the Pl\"ucker algebra with the structure of an algebra with straightening laws (ASL). In this paper, we study quadratically generated projections of the Grassmannian of lines . We then combinatorially characterize the Gorenstein ASL subalgebras of the Pl\"ucker algebra of .
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation · Advanced Combinatorial Mathematics
