Elimination ideals of Plücker ideals and algebras with straightening laws
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917195077910528 |
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| author | Borovik, Viktoriia Hibi, Takayuki |
| author_facet | Borovik, Viktoriia Hibi, Takayuki |
| contents | It is well known that the Plücker ideal defining the Grassmannian is generated by quadratic Plücker relations. These relations form a reverse lexicographic Gröbner basis and endow the Plücker algebra with the structure of an algebra with straightening laws (ASL). In this paper, we study quadratically generated projections of the Grassmannian of lines $\mathrm{Gr}(2,n)$. We then combinatorially characterize the Gorenstein ASL subalgebras of the Plücker algebra of $\mathrm{Gr}(2,n)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06897 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Elimination ideals of Plücker ideals and algebras with straightening laws Borovik, Viktoriia Hibi, Takayuki Commutative Algebra Combinatorics 13H10, 14M15, 06D05 It is well known that the Plücker ideal defining the Grassmannian is generated by quadratic Plücker relations. These relations form a reverse lexicographic Gröbner basis and endow the Plücker algebra with the structure of an algebra with straightening laws (ASL). In this paper, we study quadratically generated projections of the Grassmannian of lines $\mathrm{Gr}(2,n)$. We then combinatorially characterize the Gorenstein ASL subalgebras of the Plücker algebra of $\mathrm{Gr}(2,n)$. |
| title | Elimination ideals of Plücker ideals and algebras with straightening laws |
| topic | Commutative Algebra Combinatorics 13H10, 14M15, 06D05 |
| url | https://arxiv.org/abs/2601.06897 |