Reconstructing orbit closures from their boundaries
arXiv:2011.08807
Abstract
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.
arXiv commentv2: Added Lemmas 3.27 and 3.28 and Corollary 3.29; rewrote the proofs of Lemmas 2.3 and 6.10 and Sublemma 6.17; minor clarifications throughout
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