Computing Galois groups of Fano problems

A Fano problem consists of enumerating linear spaces a fixed dimension on variety, generalizing the classical 27 lines cubic surface. Those problems with finitely many have an associated Galois group that acts these and controls complexity computing them in suitable coordinates. These groups were first defined studied by Jordan, who particular considered P3 Recently, Hashimoto Kadets determined for special family showed all other contains alternating group. complete classification rests determination groups. We use computational tools to prove several moderate size equal symmetric group, each which previously unknown.