11 problems

Let $V$ be a subspace with coordinate projections $\pi_{E \setminus i}$, and let $Y_V \subset \prod_{i=1}^N \mathbb{P}^{n_i}$ be the associated Schubert variety. Suppose that the s…

Suppose that $W_1,W_2,\dots,W_t$ are subspaces of an $n$-dimensional $\mathbb{K}$-vector space $W\cong \mathbb{K}^n$, and let…

Let ${\cal G}$ be an $\mathbb R$-rational building set. A real subspace $C\in{\cal C}_{\cal G}$ is purely complex when it decomposes as … Write $\mathbb R({\cal G})$ for the real s…

Let ${\cal G}$ be a building set whose maximal element has the stated forest filtration … The filtration should in fact be the sequence of skeletons of a regular cell complex. This…

Let $k={\mathbb{C}}$, let $m\geq 2$, and consider the generators of the ideal in Theorem Li–Li analogue, namely … Here the ideal defines the set of points in ${\mathbb{C}}^n$ for w…

Let $Y_V \subset \mathbb{P}^{\mathbf n}$ be a Schubert variety of a subspace arrangement, and write its Chow class as … For a basis $\mathbf b=(b_1,\ldots,b_N)$, Chow-class coeffic…

Let $V_1,V_2,\ldots,V_n\subset \mathbb{C}^\ell$ be $k$-dimensional subspaces such that $V_i\cap V_{i'}=\{\boldsymbol{0}\}$ for all $i\neq i'\in[n]$. Suppose that, for every…

Let $s$ be a positive integer and let $b$ be a complex parameter. For the partition … let $Y_\lambda$ denote the associated quotient arrangement. Generic Cohen–Macaulayness conject…

Let $b,r,s,q$ be positive integers with $q\geq 2$, and let … Let $Y_\lambda$ denote the associated quotient arrangement. Quotient non-Cohen–Macaulayness conjecture. The variety…

Let $b>c$ and let $q,r,s$ be positive integers. For the partition … let $X_\lambda$ denote the associated subspace arrangement. Three-part non-Cohen–Macaulayness conjecture. If…

Let $W$ be a finite real reflection group, and let $\mathscr{P}$ be a collection of rank $2$ parabolic subgroups of $W$ closed under conjugation. Set … Define a Coxeter group $W'$…