  We introduce and study diamonds of GL(2,R)-invariant subvarieties of Abelian
and quadratic differentials, which allow us to recover information on an
invariant subvariety by simultaneously considering two degenerations, and which
provide a new tool for the classification of invariant subvarieties. We
classify a surprisingly rich collection of diamonds where the two degenerations
are contained in trivial invariant subvarieties. Our main results have been
applied to classify large collections of invariant subvarieties; the statement
of those results do not involve diamonds, but their proofs rely on them.
