9 problems

Flat-locus dimension conjecture. A tuple $f\in R^{\iota}_{\bf d}$ is in the flat locus of $\pi$ if and only if

Plücker-dimension conjecture. For every $M\in{\rm Rep}_{\bf d}$,

Homomorphism-dimension conjecture. Under either condition, $\dim\Gr_{\dim P}(M)=\langle\dim P,\dim I\rangle$ if and only if

Type A minimal-dimension conjecture. There exists a representation $M^2$ of dimension $\dim P$ such that $\Gr_{\dim P}(N)$, for $N\in{\rm Rep}_{\bf d}$, has dimension…

Irreducible-locus conjecture. There exists a representation $M^1$ of dimension $\dim P$ such that, for $N\in{\rm Rep}_{\bf d}$, the quiver Grassmannian $\Gr_{\dim P}(N)$ is irreduc…

Reduced scheme conjecture. For every principal quiver Grassmannian, the scheme structure defined by the quadratic relations corresponding to all paths in $Q$ is reduced.

Let $Q$ be a quiver and let $v_1,\ldots,v_n$ be a sequence of mutations. For each vertex $i$, let $\phi_{n,i}$ be the representation on the base quiver corresponding to the last mu…

Let $T$ be a tree extension of $S$, and let $M$ be a $T$-module such that $M_\alpha$ is an isomorphism for all arrows $\alpha$ in $T-S$. Let $M_S$ be the restriction of $M$ to $S$,…

Let $Q$ be an affine quiver of affine type, let $\lambda displaystylein \mathbb P^10(Q)$, and let $E$ be a quasi-simple module in an exceptional tube. For a dimension vector…