Collapsing K3 Surfaces, Tropical Geometry and Moduli Compactifications of Satake, Morgan-Shalen Type / Yuji Odaka, Yoshiki Oshima.

Format:

Book

Author/Creator:

Odaka, Yuji, author.

Oshima, Yoshiki, author.

Language:

English

Subjects (All):

Geometry, Algebraic.

Surfaces, Algebraic.

Physical Description:

1 online resource (165 pages)

Place of Publication:

Tokyo, Japan : Mathematical Society of Japan, 2021.

Summary:

This research monograph mainly discusses a canonical and explicit compactification of the moduli spaces of abelian varieties, K3 surfaces and compact hyperKähler varieties. For that, we use two theories of compactification－Satake compactifications for locally symmetric spaces in terms of the Lie theory, and Morgan-Shalen compactifications of complex varieties in terms of valuations.

Contents:

Chapter 1. Introduction

Chapter 2. Compactifications of Hermitian locally symmetric spaces

Chapter 3. Abelian varieties case

Chapter 4. Algebraic K3 surfaces case

Chapter 5. Uniform adiabatic limits of the metrized K3 surfaces

Chapter 6. General Kähler K3 surfaces case

Chapter 7. The moduli of tropical K3 surfaces and elliptic K3 surfaces

Chapter 8. Higher dimensional hyperKähler varieties case

Chapter 9. Towards general K-trivial varieties case

Summary of notations

Bibliography.

Notes:

Description based on publisher supplied metadata and other sources.

Includes bibliographical references.