代数曲线几何-第2卷 第2分册
代数曲线几何-第2卷 第2分册作者:阿尔巴雷洛 开 本:24开 书号ISBN:9787510077777 定价:99.0 出版时间:2014-08-01 出版社:世界图书出版公司 |
8.The Picard group of the hyperelliptic locus
9.Bibliographical notes and further reading
Chapter ⅩⅣ.Projectivity of the moduli space of stable
1.Introduction
2.A little invariant theory
3.The invariant-theoretic stability of linearly stable smooth curves
4.Numerical inequalities for families of stable curves
5.Projectivity of moduli spaces
6.Bibliographical notes and further reading
Chapter ⅩⅤ.The Teichmuller point of view
1.Introduction
2.Teichmuller space and the mapping class group
3.A little surface topology
4.Quadratic differentials and Teichmuller deformations
5.The geometry associated to a quadratic differential
6.The proof of Teichmuller's uniqueness theorem
7.Simple connectedness of the moduli stack of stable curves
8.Going to the boundary of Teichmuller space
9.Bibliographical notes and further reading
10.Exercises
Chapter ⅩⅥ.Smooth Galois covers of moduli spaces
1.Introduction
2.Level structures on smooth curves
3.Automorphisms of stable curves
4.Compactifying moduli of curves with level structure, a first attempt
5.Admissible G-covers
6.Automorphisms of admissible covers
7.Smooth covers of Mq
8.Totally unimodular lattices
9.Smooth covers of Mg,n
10.Bibliographical notes and further reading
11.Exercises
Chapter ⅩⅦ.Cycles in the moduli spaces of stable curves
1.Introduction
2.Algebraic cycles on quotients by finite groups
3.Tautological classes on moduli spaces of curves
4.Tautological relations and the tautological ring
5.Mumford's relations for the Hodge classes
6.Further considerations on cycles on moduli spaces
7.The Chow ring of MO,P
8.Bibliographical notes and further reading
9.Exercises
Chapter ⅩⅧ.Cellular decomposition of moduli spaces
1.Introduction
2.The arc system complex
3.Ribbon graphs
4.The idea behind the cellular decomposition of Mg,n
5.Uniformization
6.Hyperbolic geometry
7.The hyperbolic spine and the definition ofψ
8.The equivariant cellular decomposition of Teichmuller space
9.Stable ribbon graphs
10.Extending the cellular decomposition to a partial compactification of Teichmuller space
11.The continuity of ψ
12.Odds and ends
13.Bibliographical notes and further reading
Chapter ⅪⅩ.First consequences of the cellular decomposition
1.Introduction
2.The vanishing theorems for the rational homology of Mg,p
3.Comparing the cohomology of Mg,n to the one of its boundary strata
4.The second rational cohomology group of Mg,n
5.A quick overview of the stable rational cohomology of Mg,n and the computation of H1(Mg,n) and H2(Mg.n)
6.A closer look at the orbicell decomposition of moduli spaces
7.Combinatorial expression for the classes ψi
8.A volume computation
自然科学 数学 几何与拓扑
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