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Handbook of Moduli, Volume III

Gavril Farkas and Ian Morrison, editors
International Press
Publication Date: 
Number of Pages: 
[Reviewed by
Fernando Q. Gouvêa
, on

See the page for Handbook of Moduli, Volume I.

Volume I

Gavril Farkas and Ian Morrison

Logarithmic geometry and moduli
Dan Abramovich, Qile Chen, Danny Gillam, Yuhao Huang, Martin Olsson, Matthew Satriano and Shenghao Sun

Invariant Hilbert schemes
Michel Brion

Algebraic and tropical curves: comparing their moduli spaces
Lucia Caporaso

A superficial working guide to deformations and moduli
F. Catanese

Moduli spaces of hyperbolic surfaces and their Weil–Petersson volumes
Norman Do

Equivariant geometry and the cohomology of the moduli space of curves
Dan Edidin

Tautological and non-tautological cohomology of the moduli space of curves
C. Faber and R. Pandharipande

Alternate compactifications of moduli spaces of curves
Maksym Fedorchuk and David Ishii Smyth

The cohomology of the moduli space of Abelian varieties
Gerard van der Geer

Moduli of K3 surfaces and irreducible symplectic manifolds
V. Gritsenko, K. Hulek and G.K. Sankaran

Normal functions and the geometry of moduli spaces of curves
Richard Hain

Volume II

Parameter spaces of curves
Joe Harris

Global topology of the Hitchin system
Tás Hausel

Differential forms on singular spaces, the minimal model program, and hyperbolicity of moduli stacks
Stefan Kebekus

Contractible extremal rays on \(\mathcal{M}_{0,n}\)
Seán Keel and James McKernan

Moduli of varieties of general type
János Kollár

Singularities of stable varieties
Sándor J Kovács

Soliton equations and the Riemann-Schottky problem
I. Krichever and T. Shiota

GIT and moduli with a twist
Radu Laza

Good degenerations of moduli spaces
Jun Li

Localization in Gromov-Witten theory and Orbifold Gromov-Witten theory
Chiu-Chu Melissa Liu

From WZW models to modular functors
Eduard Looijenga

Shimura varieties and moduli
J.S. Milne

The Torelli locus and special subvarieties
Ben Moonen and Frans Oort

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