VolumeⅠ

Preface

Carrril Farkas and Ian Morrison

Logarithmic geometry and moduli

Dan Abramovich, Q/le Chen, Danny Gillam, Yuhao Huang, Martin Olsson,

Invariant Hilbert schemes

Algebraic and tropical curves: comparing their moduli spaces

A superficial working guide to deformations and moduli

Moduli spaces of hyperbolic surfaces and their Weil-Petersson volumes

Equivariant geometry and the cohomology of the moduli space of curves

Tautological and non-tautological cohomology of the moduli space of curves

Alternate compactifications of moduli spaces of curves

The cohomology of the moduli space ofAbelian varieties

Moduli of K3 surfaces and irreduable symplectic manifolds

Normal functions and the geometry of moduli spaces of curves

Volume Ⅱ

Parameter spaces of curves

Global topology of the Hitchin system

Differential forms on singular spaces, the minimal model program, and hyperboliaty of moduli stacks

Contractible extremal rays on MO,n

Moduli of varieties of general type

Singularities of stable varieties

Soliton equations and the Riemann-Schottky problem

GIT and moduli with a twist

Good degenerations of moduli spaces

Localization in Gromov-Witten theory and Orbifold Gromov-Witten theory

From WZW models to modular functors

Shimura varieties and moduli

The Torelli locus and special subvarieties

Volume Ⅲ

Birational geometry for nilpotent orbits

Yoshinori Namikawa

Cell decompositions of moduli space, lattice points and Hurwitz problems

Paul Norbury

Moduli of abelian varieties in mixed and in positive characteristic

Frans Oort

Local models of Shimura varieties, I. Geometry and combinatorics

Georgios Pappas, Michael Rapoport and Brian Smithling

Generalized theta linear series on moduli spaces of vector bundles on curves

Mihnea Popa

Computer aided unirationality proofs of moduli spaces

Frank-Olaf Schreyer

Deformation theory from the point of view of fibered categories

Mattia Talpo and Angelo Vistoli

Mumford's conjecture -- a topological outlook

Ulrike Tillmann

Rational parametrizations of moduli spaces of curves

Alessandro Verra

Hodge loci

Claire Voisin

Homological stability for mapping class groups of surfaces

Nathalie Wahl

代数几何和算术代数几何是现代数学的重要分支，与数学的许多分支有着广泛的联系，如数论、解析几何、微分几何、交换代数、代数群、拓扑学等。代数几何是任何一个希望在数学学科有所作为的学生和研究人员需要了解的一门学科，而模空间是代数几何最重要的一类对象。

《模手册(卷Ⅲ)(精)》是由50多位活跃在代数几何领域的世界知名专家撰写的综述性文章组成，由法卡斯、莫里森主编。每一篇文章针对一个专题，作者力求将第一手、最新鲜的材料呈现给读者，通过介绍该专题中基础知识、例子和结论，带领读者快速进入该领域，并了解领域内重要问题；同时介绍最新的进展，使得读者能够很快捕捉到该领域最主要的文献。