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1.

図書
図書
1. An invitation to quantum cohomology : Kontsevich's formula for rational plane curves
Joachim Kock, Israel Vainsencher
出版情報: Boston : Birkhäuser, c2007  xii, 159 p. ; 25 cm
シリーズ名: Progress in mathematics ; v. 249
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目次情報: 続きを見る
Preface
Introduction
Prologue: Warming up with Cross Ratios, and the Definition of Moduli Space / 0：
Cross ratios / 0.1：
Definition of moduli space / 0.2：
Stable n-pointed Curves / 1：
n-pointed smooth rational curves / 1.1：
Stable n-pointed rational curves / 1.2：
Stabilization, forgetting marks, contraction / 1.3：
Sketch of the construction of [Characters not reproducible subscript 0,n] / 1.4：
The boundary / 1.5：
Generalizations and references / 1.6：
Stable Maps / 2：
Maps P[superscript 1 Characters not reproducible] P[superscript r] / 2.1：
1-parameter families / 2.2：
Kontsevich stable maps / 2.3：
Idea of the construction of [Characters not reproducible subscript 0,n] (P[superscript r], d) / 2.4：
Evaluation maps / 2.5：
Forgetful maps / 2.6：
Easy properties and examples / 2.7：
Complete conics / 2.9：
Enumerative Geometry via Stable Maps / 2.10：
Classical enumerative geometry / 3.1：
Counting conics and rational cubics via stable maps / 3.2：
Kontsevich's formula / 3.3：
Transversality and enumerative significance / 3.4：
Stable maps versus rational curves / 3.5：
Gromov-Witten Invariants / 3.6：
Definition and enumerative interpretation / 4.1：
Properties of Gromov-Witten invariants / 4.2：
Recursion / 4.3：
The reconstruction theorem / 4.4：
Quantum Cohomology / 4.5：
Quick primer on generating functions / 5.1：
The Gromov-Witten potential and the quantum product / 5.2：
Associativity / 5.3：
Kontsevich's formula via quantum cohomology / 5.4：
Bibliography / 5.5：
Index
Preface
Introduction
Prologue: Warming up with Cross Ratios, and the Definition of Moduli Space / 0：
2.

図書
図書
2. Integration of one-forms on p-adic analytic spaces (: hard ; : pbk)
Vladimir G. Berkovich
出版情報: Princeton : Princeton University Press, c2007  vi, 156 p. ; 25 cm
シリーズ名: Annals of mathematics studies ; no. 162
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Introduction
Naive Analytic Functions and Formulation of the Main Result / 1：
Preliminary remarks and notation / 1.1：
The sheaf of naive analytic functions / 1.2：
D[subscript X]-modules and D[subscript X]-modules / 1.3：
Logarithms / 1.4：
Logarithmic Poincare lemma / 1.5：
Formulation of the main results / 1.6：
Etale Neighborhoods of a Point in a Smooth Analytic Space / 2：
Etale neighborhoods of a point with s(x) = dim(X) / 2.1：
The local structure of a smooth analytic curve / 2.2：
Etale neighborhoods of a point with s(x) < dim(X) / 2.3：
Basic curves / 2.4：
Properties of Strictly Poly-stable and Marked Formal Schemes / 3：
Strictly poly-stable formal schemes / 3.1：
Open neighborhoods of the generic point of an irreducible component / 3.2：
A property of strata / 3.3：
A tubular neighborhood of the diagonal of a stratum closure / 3.4：
The same for proper marked formal schemes / 3.5：
Properties of the Sheaves [Omega Characters not reproducible]/d[Characters not reproducible subscript X] / 4：
Analytic curve connectedness of closed analytic spaces / 4.1：
The sheaves [Characters not reproducible], [Characters not reproducible], and [Characters not reproducible] / 4.2：
Structure of the sheaves [Omega Characters not reproducible]/d[Characters not reproducible subscript X] for smooth analytic curves / 4.3：
Injectivity of the homomorphism dLog : [Characters not reproducible subscript z]c[subscript X rarr Omega Character not reproducible]/d[Characters not reproducible subscript X] / 4.4：
A subsheaf [Psi subscript x] [Characters not reproducible] [Omega Characters not reproducible]/d[Characters not reproducible subscript X] and a subspace V[subscript X,x Characters not reproducible Omega Characters not reproducible]]/d[Characters not reproducible subscript X,x] / 4.5：
Isocrystals / 5：
Wide germs of analytic spaces and of formal schemes / 5.1：
D-modules on smooth strictly k-affinoid germs and isocrystals / 5.2：
A construction of isocrystals / 5.3：
The filtered isocrystals E[subscript B] and the shuffle algebras / 5.4：
Unipotent isocrystals E[superscript i] (X, [Characters not reproducible]) / 5.5：
F-isocrystals / 6：
Frobenius liftings / 6.1：
A Frobenius structure on the isocrystals E[superscript i] (X,[Characters not reproducible]) / 6.2：
A uniqueness property of certain F-isocrystals / 6.3：
Structure of a commutative filtered D[subscript B]-algebra on E(X, [Characters not reproducible]) / 6.4：
Filtered F-isocrystals E[superscript K](X, [Characters not reproducible]) and F[superscript lambda] ([Characters not reproducible], [Characters not reproducible]) / 6.5：
Construction of the Sheaves S[Characters not reproducible] / 7：
Induction hypotheses / 7.1：
Split one-forms / 7.2：
Marked and weakly marked one-forms / 7.3：
Construction of a primitive of a weakly marked one-form / 7.4：
Construction of the D[subscript X]-modules S[Characters not reproducible] / 7.5：
End of the proof / 7.6：
Properties of the sheaves S[Characters not reproducible] / 8：
Filtered D[subscript (X,Y)]-algebras [epsiv superscript lambda](X, Y) for germs with good reduction / 8.1：
Filtered D[subscript Characters not reproducible]-algebras [epsiv superscript lambda]([Characters not reproducible]) for proper marked formal schemes / 8.2：
A filtered D[subscript Characters not reproducible subscript X,x]]-subalgebra [epsiv Characters not reproducible] S[Characters not reproducible] and the space V[subscript X,x] / 8.3：
More uniqueness properties / 8.4：
A filtered D[subscript X]-subalgebra s[subscript X Characters not reproducible] S[subscript X] and the sheaf [Psi subscript X] / 8.5：
Integration and Parallel Transport along a Path / 9：
Integration of closed one-forms along a path / 9.1：
Nontrivial dependence on the homotopy class of a path / 9.2：
Locally unipotent and quasi-unipotent D[subscript X]-modules / 9.3：
Parallel transport along a path / 9.4：
Parallel transport along an etale path / 9.5：
References
Index of Notation
Index of Terminology
Introduction
Naive Analytic Functions and Formulation of the Main Result / 1：
Preliminary remarks and notation / 1.1：
3.

図書
図書
3. Handbook of tilting theory (: pbk)
edited by Lidia Angeleri Hügel, Dieter Happel, Henning Krause
出版情報: Cambridge, UK : Cambridge University Press, 2007  viii. 472 ; 23 cm
シリーズ名: London Mathematical Society lecture note series ; 332
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4.

図書
図書
4. Quantum stochastic processes and noncommutative geometry (: hbk.)
Kalyan B. Sinha, Debashish Goswami
出版情報: Cambridge : Cambridge University Press, 2007  x, 290 p. ; 24 cm
シリーズ名: Cambridge tracts in mathematics ; 169
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5.

図書
図書
5. Curve and surface reconstruction : algorithms with mathematical analysis
Tamal K. Dey
出版情報: New York : Cambridge University Press, 2007  xiii, 214 p. ; 24 cm
シリーズ名: Cambridge monographs on applied and computational mathematics ; 23
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目次情報: 続きを見る
Preface
Basics / 1：
Shapes / 1.1：
Spaces and Maps / 1.1.1：
Manifolds / 1.1.2：
Complexes / 1.1.3：
Feature Size and Sampling / 1.2：
Medial Axis / 1.2.1：
Local Feature Size / 1.2.2：
Sampling / 1.2.3：
Voronoi Diagram and Delaunay Triangulation / 1.3：
Two Dimensions / 1.3.1：
Three Dimensions / 1.3.2：
Notes and Exercises / 1.4：
Exercises
Curve Reconstruction / 2：
Consequences of [epsilon]-Sampling / 2.1：
Crust / 2.2：
Algorithm / 2.2.1：
Correctness / 2.2.2：
NN-Crust / 2.3：
Surface Samples / 2.3.1：
Normals / 3.1：
Approximation of Normals / 3.1.1：
Normal Variation / 3.1.2：
Edge and Triangle Normals / 3.1.3：
Topology / 3.2：
Topological Ball Property / 3.2.1：
Voronoi Faces / 3.2.2：
Surface Reconstruction / 3.3：
Poles and Cocones / 4.1：
Cocone Triangles / 4.1.2：
Pruning / 4.1.3：
Manifold Extraction / 4.1.4：
Geometric Guarantees / 4.2：
Additional Properties / 4.2.1：
Topological Guarantee / 4.3：
The Map [nu] / 4.3.1：
Homeomorphism Proof / 4.3.2：
Undersampling / 4.4：
Samples and Boundaries / 5.1：
Boundary Sample Points / 5.1.1：
Flat Sample Points / 5.1.2：
Flatness Analysis / 5.2：
Boundary Detection / 5.3：
Justification / 5.3.1：
Reconstruction / 5.3.2：
Watertight Reconstructions / 5.4：
Power Crust / 6.1：
Definition / 6.1.1：
Proximity / 6.1.2：
Homeomorphism and Isotopy / 6.1.3：
Tight Cocone / 6.1.4：
Marking / 6.2.1：
Peeling / 6.2.2：
Experimental Results / 6.3：
Noisy Samples / 6.4：
Noise Model / 7.1：
Empty Balls / 7.2：
Normal Approximation / 7.3：
Analysis / 7.3.1：
Feature Approximation / 7.3.2：
Noise and Reconstruction / 7.4.1：
Preliminaries / 8.1：
Union of Balls / 8.2：
Topological Equivalence / 8.3：
Labeling / 8.4.1：
Implicit Surface-Based Reconstructions / 8.4.2：
Generic Approach / 9.1：
Implicit Function Properties / 9.1.1：
MLS Surfaces / 9.1.2：
Adaptive MLS Surfaces / 9.2.1：
Sampling Assumptions and Consequences / 9.3：
Influence of Samples / 9.3.1：
Surface Properties / 9.4：
Hausdorff Property / 9.4.1：
Gradient Property / 9.4.2：
Algorithm and Implementation / 9.5：
Normal and Feature Approximation / 9.5.1：
Projection / 9.5.2：
Other MLS Surfaces / 9.6：
Projection MLS / 9.6.1：
Variation / 9.6.2：
Computational Issues / 9.6.3：
Voronoi-Based Implicit Surface / 9.7：
Morse Theoretic Reconstructions / 9.8：
Morse Functions and Flows / 10.1：
Discretization / 10.2：
Vector Field / 10.2.1：
Discrete Flow / 10.2.2：
Relations to Voronoi/Delaunay Diagrams / 10.2.3：
Reconstruction with Flow Complex / 10.3：
Flow Complex Construction / 10.3.1：
Merging / 10.3.2：
Critical Point Separation / 10.3.3：
Reconstruction with a Delaunay Subcomplex / 10.4：
Distance from Delaunay Balls / 10.4.1：
Classifying and Ordering Simplices / 10.4.2：
Bibliography / 10.4.3：
Index
Preface
Basics / 1：
Shapes / 1.1：
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