Reconstructing orbit closures from their boundaries / Paul Apisa, Alex Wright.

Format:

Book

Author/Creator:

Apisa, Paul, author.

Wright, Alex (Alexander Murray), author.

Series:

Memoirs of the American Mathematical Society ; no. 1487.

Memoirs of the American Mathematical Society, 0065-9266 ; no. 1487

Language:

English

Subjects (All):

Dynamics.

Topology.

Physical Description:

v, 141 pages : illustrations ; 26 cm.

Place of Publication:

Providence, RI : American Mathematical Society, 2024.

Summary:

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.

Contents:

Chapter 1. Introduction

Chapter 2. The Diamond Lemma

Chapter 3. Preliminaries on orbit closures

Chapter 4. Preliminaries on strata

Chapter 5. Diamonds with a stratum of Abelian differentials

Chapter 6. Gluing in a complex envelope

Chapter 7. Diamonds with quadratic doubles

Chapter 8. Diamonds of full loci of covers

Chapter 9. Hyperelliptic components

Chapter 10. Diamonds with Abelian and quadratic doubles

Bibliography.

Notes:

Includes bibliographical references (pages 139-141).

ISBN:

1470469111

9781470469115

OCLC:

1449624065