The geometric naturality of Schubert polynomials and their combinatorial pipe dream
representations was established by Knutson and Miller (2005) via antidiagonal Gröbner …

Let Matn× n be the space of n× n matrices over a field k; the coordinate ring is R= k [xij] 1≤ i,
j≤ n. Let GLn be the general linear group of invertible n× n matrices with a Borel subgroup B …

In this paper, we survey the theory of Cartwright–Sturmfels ideals. These are ℤ n-graded
ideals, whose multigraded generic initial ideal is radical. Cartwright–Sturmfels ideals have …

Geometric vertex decomposition and liaison are two frameworks that have been used to
produce similar results about similar families of algebraic varieties. In this paper, we …

We give a criterion for a collection of polynomials to be a universal Gröbner basis for an
ideal in terms of the multidegree of the closure of the corresponding affine variety in (P1) N …

The geometric vertex decomposability property for polynomial ideals is an ideal-theoretic
generalization of the vertex decomposability property for simplicial complexes. Indeed, a …

We prove a criterion of when the dual character $\chi_ {D}(x) $ of the flagged Weyl module
associated to a diagram $ D $ in the grid $[n]\times [n] $ is zero-one, that is, the coefficients …

We study the Castelnuovo-Mumford regularity of tangent cones of Schubert varieties.
Conjectures about this statistic are presented; these are proved for the covexillary case. This …

arXiv:2303.01436v1 [math.AG] 2 Mar 2023 Page 1 arXiv:2303.01436v1 [math.AG] 2 Mar
2023 SCHUBERT GEOMETRY AND COMBINATORICS ALEXANDER WOO AND …

We study the back stable-theory Schubert calculus of the infinite flag variety. We define back
stable (double) Grothendieck polynomials and double-Stanley functions and establish …