Year: 2026
Type: preprint
Abstract: Let $C(v)$ denote a Schubert cell in the flag variety $\operatorname{GL}_n/B$, and let $X(w)$ be a Schubert variety containing $C(v)$. Mellit has conjectured that, if $X(w)$ is smooth, the existence of an open $B$-orbit in the conormal bundle to $C(v)$ in $X(w)$ is equivalent to $C(w_0w)$ being contained in the smooth locus of $X(w_0v)$. We prove a stronger version of this conjecture, requiring only that $X(w)$ is factorial. We prove our result by constructing a sequence of graphs associated to the pair $v,w$ such that the existence of a cycle in one of these graphs is equivalent to the non-existence of such an open orbit.
Source: arXiv (Cornell University)
Author: Aoki, Derek R.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7224106636