Application of Lie groups to the search for symmetries of implicit planar webs (Q6652170)

\textit{A. Hénaut} [J. Math. Sci., Tokyo 29, No. 1, 115--148 (2022; Zbl 1507.14014.)] studied symmetries for complex \(d\)-webs defined in \(\mathbb{C}^{2}\) implicitly, i.e., given as solutions of an analytic first order differential equation with \(y'\)-degree \(d\)\N\N\[F(x,y,y')= a_{0}(x,y)(y')^{d}+\ldots + a_{d-1}(x,y) y'+a_{d}(x,y) =0\]\N\NHe used both algebraic and differential geometric tools.\N\NThe authors give new proofs of some of the results obtained in that paper, using the framework of actions of Lie groups on differential equations. Besides they specify the existing link between the Lie algebra of symmetries of a given web and the existence of Darboux polynomials. The paper is very well written and several symmetry groups for known webs are explicitly computed, such as those of parallel, Clairaut and Zariski webs, and those of hexagonal 3-webs.