代數(shù)兒何和算：術(shù)代數(shù)幾何是現(xiàn)代數(shù)學(xué)的重要分支，與數(shù)學(xué)的許多分支有著廣泛的聯(lián)系，如數(shù)論、解析兒何、微分幾何、交換代數(shù)、代數(shù)群、拓?fù)鋵W(xué)等。代數(shù)幾何是任何一個(gè)希望在數(shù)學(xué)學(xué)科有所作為的學(xué)生和研究人員需要了解的一門學(xué)科，而模空間足代數(shù)幾何最重要的一類對(duì)象。
《模手冊(cè)（卷1）（英文版）》是由50多位活躍在代數(shù)幾何領(lǐng)域的世界知名專家撰寫的綜述性文章組成。每一篇文章針對(duì)一個(gè)專題，作者力求將第一手、最新鮮的材料呈現(xiàn)給讀者，通過(guò)介紹該專題中基礎(chǔ)知識(shí)、例子和結(jié)論、帶領(lǐng)讀者快速進(jìn)入該領(lǐng)域，并了解領(lǐng)域內(nèi)重要問(wèn)題；同時(shí)介紹最新的進(jìn)展，使得讀者能夠很快捕捉劍該領(lǐng)域最主要的文獻(xiàn)
Volume Ⅰ
Preface
Gavril Farkas and Ian Morrison
Logarithmic geometry and moduli
Dan Abramovich, Qile Chen, Danny Cillam, 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 superfiaal 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
Volume Ⅰ
Preface
Gavril Farkas and Ian Morrison
Logarithmic geometry and moduli
Dan Abramovich, Qile Chen, Danny Cillam, 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 superfiaal 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 compaaifications of moduli spaces of curves
Maksym Fedorchuk and David Ishii Smyth
The cohomology of the moduli space ofAbelian varieties
Gerard van der Geer
Moduli of K3 surfaces and irreduable symplectic manifolds
V Gritsenko, K. Hulek and C.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
Tamas Hausel
Differential forms on singular spaces, the minimal model program, and hyperboliaty of moduli stacks
Stefan Kebekus
Contractible extremal rays on Mo,n
Sean Keel and James McKernan
Moduli of varieties of general type
Janos Kollar
Singularities of stable varieties
Sandor J Kovacs
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
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