Some algebraic properties of ASM varieties
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915727008595968 |
|---|---|
| author | Axelrod-Freed, Ilani Hao, Hanson Kendall, Matthew Klein, Patricia Luo, Yuyuan |
| author_facet | Axelrod-Freed, Ilani Hao, Hanson Kendall, Matthew Klein, Patricia Luo, Yuyuan |
| contents | Fulton's matrix Schubert varieties are affine varieties that arise in the study of Schubert calculus in the complete flag variety. Weigandt showed that arbitrary intersections of matrix Schubert varieties, now called ASM varieties, are indexed by alternating sign matrices (ASMs), objects with a long history in enumerative combinatorics. It is very difficult to assess Cohen-Macaulayness of ASM varieties or to compute their codimension, though these properties are well understood for matrix Schubert varieties due to work of Fulton. In this paper we study these properties of ASM varieties with a focus on the relationship between a pair of ASMs and their direct sum. We also consider ASM pattern avoidance from an algebro-geometric perspective. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_10480 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some algebraic properties of ASM varieties Axelrod-Freed, Ilani Hao, Hanson Kendall, Matthew Klein, Patricia Luo, Yuyuan Combinatorics Commutative Algebra 05E14, 14M12, 14M15, 05A05 Fulton's matrix Schubert varieties are affine varieties that arise in the study of Schubert calculus in the complete flag variety. Weigandt showed that arbitrary intersections of matrix Schubert varieties, now called ASM varieties, are indexed by alternating sign matrices (ASMs), objects with a long history in enumerative combinatorics. It is very difficult to assess Cohen-Macaulayness of ASM varieties or to compute their codimension, though these properties are well understood for matrix Schubert varieties due to work of Fulton. In this paper we study these properties of ASM varieties with a focus on the relationship between a pair of ASMs and their direct sum. We also consider ASM pattern avoidance from an algebro-geometric perspective. |
| title | Some algebraic properties of ASM varieties |
| topic | Combinatorics Commutative Algebra 05E14, 14M12, 14M15, 05A05 |
| url | https://arxiv.org/abs/2505.10480 |