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1.

図書
図書
1. Discrete integrable geometry and physics (: hc)
edited by Alexander I. Bobenko and Ruedi Seiler
出版情報: New York : Oxford University Press, 1999  xxvii, 370 p. ; 25 cm
シリーズ名: Oxford lecture series in mathematics and its applications ; 16
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目次情報: 続きを見る
List of contributors
Introduction / Alexander I. Bobenko ; Ruedi Seiler
Geometry / I：
Discretization of Surfaces and Integrable Systems / Ulrich Pinkall1：
A Discrete Version of the Darboux Transform for Isothermic Surfaces / Udo Hertrich-Jeromin ; Tim Hoffmann2：
Discrete Amsler Surfaces and a Discrete Painleve III Equation / 3：
Discrete cmc Surfaces and Discrete Holomorphic Maps / 4：
Discrete Indefinite Affine Spheres / Wolfgang K. Schief5：
Geometry of Discrete Curves and Lattices and Integrable Difference Equations / Adam Doliwa ; Paolo Maria Santini6：
Classical Systems / II：
R-matrices and Integrable Discretizations / Yuri B. Suris7：
Discrete Painleve Equations and Symmetry Reduction on the Lattice / Frank W. Nijhoff8：
Lagrangian Description of Doubly Discrete Sine-Gordon Type Models / Nadja Kutz9：
Quantum Systems / III：
Spectra of Quantum Integrals / Johannes Kellendonk10：
Algebraic Quantization of Integrable Models in Discrete Space-Time / Ludwig D. Faddeev ; Alexander Yu. Volkov11：
Affine Toda Field Theory as a Three-dimensional Integrable System / Rinat M. Kashaev ; Nikolai Yu. Reshetikhin12：
Quantum Hyperbolic Invariants of Knots / 13：
Charge Transport in the Discretized Landau Model / Thomas Richter14：
Index
List of contributors
Introduction / Alexander I. Bobenko ; Ruedi Seiler
Geometry / I：
2.

図書
図書
2. Mirror symmetry and algebraic geometry (: pbk)
David A. Cox, Sheldon Katz
出版情報: Providence, R.I. : American Mathematical Society, c1999  xxi, 469 p. ; 26 cm
シリーズ名: Mathematical surveys and monographs ; v. 68
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目次情報: 続きを見る
Introduction
The quintic threefold
Toric geometry Mirror symmetry constructions
Hodge theory and Yukawa couplings
Moduli spaces Gromov-Witten invariants
Quantum cohomology Localization
Quantum differential equations
The mirror theorem Conclusion
Singular varieties
Physical theories
Bibliography
Index
Introduction
The quintic threefold
Toric geometry Mirror symmetry constructions
3.

図書
図書
3. The red book of varieties and schemes. 2nd., expanded ed
David Mumford
出版情報: Berlin ; Tokyo : Springer-Verlag, c1999  x, 304 p. ; 25 cm
シリーズ名: Lecture notes in mathematics ; 1358
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Preface to the Second Edition
Preface to the First Edition
Varieties / I：
Some algebra / 1：
Irreducible algebraic sets / 2：
Definition of a morphism / 3：
Sheaves and affi ne varieties / 4：
Definition of prevarieties and morphisms / 5：
Products and the Hausdorff Axiom / 6：
Dimension / 7：
The fibres of a morphism / 8：
Complete varieties / 9：
Complex varieties / 10：
Preschemes / II：
Spec (R)
The category of preschemes
Varieties and preschemes
Fields of definition
Closed subpreschemes
The functor of points of a prescheme
Proper morphisms and finite morphisms
Specialization
Local Properties of Schemes / III：
Quasi-coherent modules
Coherent modules
Tangent cones
Non-singularity and differentials
Étale morphisms
Uniformizing parameters
Non-singularity and the UFD property
Normal varieties and normalization
Zariski's Main Theorem
Flat and smooth morphisms
Appendix: Curves and Their Jacobians
What is a Curve and How Explicitly Can We Describe Them? / Lecture I：
The Moduli Space of Curves: Definition, Coordinatization, and Some Properties / Lecture II：
How Jacobians and Theta Functions Arise / Lecture III：
The Torelli Theorem and the Schottky Problem / Lecture IV：
Survey of Work on the Schottky Problem up to 1996 by Enrico Arbarello
References: The Red Book of Varieties and Schemes
Guide to the Literature and References: Curves and Their Jacobians
Supplementary Bibliography on the Schottky Problem by Enrico Arbarello
Preface to the Second Edition
Preface to the First Edition
Varieties / I：
4.

図書
図書
4. The inverse Galois problem, moduli spaces and mapping class groups (: pbk)
edited by Leila Schneps and Pierre Lochak
出版情報: Cambridge ; New York ; Melbourne : Cambridge University Press, 1997  ix, 347 p. ; 23 cm
シリーズ名: London Mathematical Society lecture note series ; 243 . Geometric Galois actions ; 2
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List of participants
Abstracts of the talks
Introduction / Part I：
Abstracts / Part II：
Dessins d'enfants / Part III：
Unicellular cartography and Galois orbits of plane trees / N. Adrianov ; G. Shabat1：
Galois groups, monodromy groups and cartographical groups / G. Jones ; M. Streit2：
Drawings, triangle groups and algebraic curves / W. Harvey3：
Permutation techniques for coset representations of modular subgroups / T. Hsu4：
On groups acting on dessin-labeled objects / V. Shabat5：
Dessins d'enfants en genre 1 / L. Zapponi6：
Inverse Galois Problem / Part IV：
The regular inverse Galois problem over large fields / P. Debes ; B. Deschamps7：
The symplectic braid group and Galois realizations / K. Strambach ; H. Volklein8：
Obstructed components of A5 modular towers / M. Fried ; Y. Kopeliovic9：
Galois Actions And Mapping Class Groups / Part V：
Monodromy of iterated integrals (non-Abelian unipotent periods) / Z. Wojtkowiak10：
Deformation of singularities and mapping class groups / M. Matsumoto11：
Universal Teichmnller Theory / Part VI：
The universal Ptolemy group and its completions / R. Penner12：
Sur l'isomorphisme du groupe de Richard Thompson avec le groupe de PtolTmTe / M. Imbert ; V. Sergiescu13：
The universal Ptolemy-Teichmuller groupoid / P. Lochak ; L. Schneps14：
List of participants
Abstracts of the talks
Introduction / Part I：
5.

図書
図書
5. Stable groups (: pbk)
Frank O. Wagner
出版情報: Cambridge ; New York : Cambridge University Press, 1997  ix, 309 p. ; 23 cm
シリーズ名: London Mathematical Society lecture note series ; 240
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6.

図書
図書
6. Fano varieties (: gw)
A.N. Parshin, I.R. Shafarevich (eds.)
出版情報: Berlin ; Tokyo : Springer-Verlag, c1999  247 p. ; 25 cm
シリーズ名: Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze ; v. 47 . Algebraic geometry ; 5
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7.

図書
図書
7. Algebraic groups and their birational invariants (: AMS soft cover)
V.E. Voskresenskiĭ ; [translated from the original Russian manuscript by Boris Kunyavski]
出版情報: Providence, R.I. : American Mathematical Society, c1998  xiii, 218 p. ; 26 cm
シリーズ名: Translations of mathematical monographs ; v. 179
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8.

図書
図書
8. Using algebraic geometry (: hard ; : pbk)
David Cox, John Little, Donal O'Shea
出版情報: New York : Springer, c1998  xii, 499 p. ; 24 cm
シリーズ名: Graduate texts in mathematics ; 185
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9.

図書
図書
9. Algebraic geometry
Daniel Bump
出版情報: Singapore ; River Edge, N.J. : World Scientific, c1998  ix, 218 p. ; 23 cm
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10.

図書
図書
10. Séminaire Bourbaki (vol. 1:Années 1948/49-1949/50-1950/51 - vol. 10:Années 1966/67-1967/68)
Bourbaki, Nicolas
出版情報: Paris : Société mathématique de France, 1995  10 v. ; 25 cm
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