4 papers
Torus actions on compactified braid varieties and polytopality of subword complexes
Lara Bossinger, Mikhail Gorsky, José Simental
Every cluster variety admits an action of its cluster dilation group. We prove that, in the case of braid varieties for simple Lie groups, this action always extends to a regular a…
Comparing cluster algebras on braid varieties
Roger Casals, Pavel Galashin, Mikhail Gorsky +3
Braid varieties parametrize linear configurations of flags with transversality conditions dictated by positive braids. They include and generalize reduced double Bruhat cells, posi…
Preorders on maximal chains: hyperplane arrangements, Cambrian lattices, and maximal green sequences
Mikhail Gorsky, Nicholas J. Williams
We study preorders on (equivalence classes of) maximal chains in the general context of polygonal lattices endowed with suitably nice edge labellings. We show that, given a quotien…
Cluster deep loci and mirror symmetry
Marco Castronovo, Mikhail Gorsky, José Simental +1
Affine cluster varieties are covered up to codimension 2 by open algebraic tori. We put forth a general conjecture (based on earlier conversation between Vivek Shende and the last…