Minimality of the $\mathcal D$-groupoid of symmetries of a projective structure

Alejandro Arenas Tirado, David Blázquez-Sanz, Guy Casale

Published 2023-09-14Version 1

In this article we study Kummer's $\mathcal D$-groupoid, which is the groupoid of symmetries of a meromorphic projective structure. We give necessary and sufficient conditions for its minimality, in the sense of not having infinite sub-$\mathcal D$-groupoids. The condition that we find turns out to be equivalent to the strong minimality of the non-linear Schwarzian equation and the non-integrability by means of Liouvillian functions of the linear Schwarzian equation.