# Invariants and meromorphic automorphic forms

**Abstract:**

The theory of period mappings leads to some remarkable isomorphisms between certain graded algebras of polynomials (in several variables) invariant under an algebraic group and certain graded algebras of meromorphic automorphic forms (also in several variables). These have their origin in equally remarkable isomorphisms between apparently distinct geometric objects. We discuss an example and the general theory that underlies this.