Work

Some algebraic properties of ASM varieties

Year: 2025

Type: article

Abstract: 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.

Source: Glasgow Mathematical Journal

DOI: 10.1017/s0017089525100840

Authors: Ilani Axelrod-Freed, Hanson Hao, Matthew Kendall, Patricia Klein, Yuyuan Luo

Institutions: Massachusetts Institute of Technology, University of California, Berkeley, Stanford University, Texas A&M University, Princeton University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: National Science Foundation, University of Minnesota