Quotient Geometry of the A6-Action on P2(C): Local Linear Models, InvariantAlgebras, and Orbifold Invariants

Abstract

We provide an explicit analytic description of the quotient sur face Y = P2(C)/A6 under the Valentiner action. Using Cartan’s lin earization and invariant algebras, we classify all local quotient models. Cyclic subgroups C2,C3,C4,C5 yield classical cyclic singularities, while D8 and D10 give non-cyclic singularities. Isotropy from V4, E9, and S3 corresponds to smooth points. Gluing these local models produces a nor mal projective surface with a completely determined singularity structure.