6 problems

For each $n$, define … where $R_{v,w}$ is the associated graded ring of the local ring of the Schubert variety $X_w$ at the torus-fixed point $e_v$. Maximal-regularity conjecture.…

Let $GL_n/B$ be the complete flag variety, with Schubert varieties $X_w$ indexed by permutations $w\in\mathfrak S_n$. For $v\leq w$ in Bruhat order, let $H_{v,w}(q)$ be the Hilbert…

Let $GL_n/B$ be the complete flag variety, with Schubert varieties $X_w$ indexed by permutations $w\in\mathfrak S_n$. For $u\leq v\leq w$ in Bruhat order, let $H_{u,w}(q)$ and…

Let $GL_n/B$ be the complete flag variety, with Schubert varieties $X_w$ indexed by permutations $w\in\mathfrak S_n$. For $v\leq w$ in Bruhat order, let $R_{v,w}$ be the associated…

Let $GL_n/B$ be the complete flag variety, with Schubert varieties $X_w$ indexed by permutations $w\in\mathfrak S_n$. For $u\leq v\leq w$ in Bruhat order, let $R_{u,w}$ and…

Regularity conjecture. The Castelnuovo–Mumford regularity satisfies