Current Developments in Hodge Theory : Proceedings of Hodge Theory at IMSA / edited by Phillip Griffiths, Ludmil Katzarkov, Carlos Simpson.

Format:

Book

Author/Creator:

Griffiths, Phillip.

Series:

Simons Symposia, 2365-9572

Language:

English

Subjects (All):

Geometry, Algebraic.

Number theory.

Algebraic Geometry.

Number Theory.

Local Subjects:

Algebraic Geometry.

Number Theory.

Physical Description:

1 online resource (683 pages)

Edition:

1st ed. 2025.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2025.

Summary:

This book brings together contributions by top-level experts from a wide range of topics in modern Hodge theory, originating in the authors’ participation in the special years on Hodge theory at the Institute of Mathematical Sciences of the Americas (IMSA) in Miami. One of the main themes is the study of moduli spaces and their compactifications. Several articles speak of the singularities occuring in the boundaries of geometrical or Hodge-theoretic compactifications, semistable reduction, the implications of canonical models for model theory in the sense of logic, and fundamental groups of moduli spaces and their associated Torelli groups. Other topics include Mukai lattices, derived moduli spaces, foliations, Higgs bundles and hyperbolicity, the study of pseudoconvexity properties of neighborhoods of infinity, contributions to the theory of degenerations and limiting mixed Hodge structures. This text will provide an indispensable reference for research mathematicians and specialist graduate students, where the modern approaches to moduli spaces are illustrated by their realizations and applications in examples of interest for the interplay between Hodge theory and moduli spaces.

Contents:

Preface

Introduction

The Coble-Mukai lattice from Q-Gorenstein deformations

Hyperbolic geometry of moduli spaces of algebraic varieties via Hodge theory, and beyond

Semistable reduction over thick log points

Degeneration of Hodge structures on I-surfaces

Foliations and stable maps

Pseudoconvexity at infinity in Hodge theory: a codimension one example

The model theory of canonical models of Shimura curves

Moduli spaces on Kuznetsov components are irreducible symplectic varieties

Mapping class groups of simply connected Kahler manifolds

Hodge theory of degenerations, (II): vanishing cohomology and geometric applications.

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

3-031-99683-6

9783031996832

OCLC:

1586562832