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出版社:高等教育
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ISBN:9787040351743
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作者:(德)法卡斯//(美)莫裡森
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頁數:583
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出版日期:2013-01-01
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印刷日期:2013-01-01
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包裝:精裝
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開本:16開
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版次:1
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印次:1
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字數:710千字
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代數幾何和算術代數幾何是現代數學的重要分支,與數學的許多分支有著廣泛的聯繫,如數論、解析幾何、微分幾何、交換代數、代數群、拓撲學等。代數幾何是任何一個希望在數學學科有所作為的學生和研究人員需要了解的一門學科,而模空間是代數幾何*重要的一類對像。 《模手冊(卷Ⅲ)(精)》是由50多位活躍在代數幾何領域的世界知名專家撰寫的綜述性文章組成,由法卡斯、莫裡森主編。每一篇文章針對一個專題,作者力求將**手、*新鮮的材料呈現給讀者,通過介紹該專題中基礎知識、例子和結論,帶領讀者快速進入該領域,並了解領域內重要問題;同時介紹*新的進展,使得讀者能夠很快捕捉到該領域*主要的文獻。
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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
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