Calabi-Yau varieties and mirror symmetry
著者
書誌事項
Calabi-Yau varieties and mirror symmetry
(Fields Institute communications, 38)
American Mathematical Society, c2003
大学図書館所蔵 全28件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references
"This volume is the proceedings of the workshop, and it presents articles on the recent developments on Calabi-Yau varieties and mirror symmetry." - Introduction
Includes Schedule of Workshops
内容説明・目次
内容説明
The idea of mirror symmetry originated in physics, but in recent years, the field of mirror symmetry has exploded onto the mathematical scene. It has inspired many new developments in algebraic and arithmetic geometry, toric geometry, the theory of Riemann surfaces, and infinite-dimensional Lie algebras among others. The developments in physics stimulated the interest of mathematicians in Calabi-Yau varieties. This led to the realization that the time is ripe for mathematicians, armed with many concrete examples and alerted by the mirror symmetry phenomenon, to focus on Calabi-Yau varieties and to test for these special varieties some of the great outstanding conjectures, e.g., the modularity conjecture for Calabi-Yau threefolds defined over the rationals, the Bloch-Beilinson conjectures, regulator maps of higher algebraic cycles, Picard-Fuchs differential equations, GKZ hypergeometric systems, and others.The articles in this volume report on current developments. The papers are divided roughly into two categories: geometric methods and arithmetic methods. One of the significant outcomes of the workshop is that we are finally beginning to understand the mirror symmetry phenomenon from the arithmetic point of view, namely, in terms of zeta-functions and L-series of mirror pairs of Calabi-Yau threefolds. The book is suitable for researchers interested in mirror symmetry and string theory.
目次
Geometric methods: Mixed toric residues and Calabi-Yau complete intersections by V. V. Batyrev and E. N. Materov Crepant resolutions of $\mathbb{C}^n/A_1(n)$ and flops of $n$-folders for $n=4,5$ by L. Chiang and S.-s. Roan Picard-Fuchs equations, integrable systems and higher algebraic K-theory by P. L. del Angel and S. Muller-Stach Counting BPS states via holomorphic anomaly equations by S. Hosono Regulators of Chow cycles on Calabi-Yau varieties by J. D. Lewis Arithmetic methods: Calabi-Yau manifolds over finite fields, II by P. Candelas, X. de la Ossa, and F. Rodriguez-Villegas Modularity of rigid Calabi-Yau threefolds over $\mathbb{Q}$ by L. Dieulefait and J. Manoharmayum $K3$ surfaces with symplectic group actions by Y. Goto Birational smooth minimal models have equal Hodge numbers in all dimensions by T. Ito The $n$th root of the mirror map by B. H. Lian and S.-T. Yau On a Shioda-Inose structure of a family of K3 surfaces by L. Long Black hole attractor varieties and complex multiplication by M. Lynker, V. Periwal, and R. Schimmrigk Hypergeometric families of Calabi-Yau manifolds by F. Rodriguez-Villegas Aspects of conformal field theory from Calabi-Yau arithmetic by R. Schimmrigk Ordinary Calabi-Yau-3 crystals by J. Stienstra The ordinary limit for varieties over $\mathbb{Z}[x_1,\ldots,x_r]$ by J. Stienstra Update on the modularity of Calabi-Yau varieties with appendix by Helena Verrill by N. Yui Problems by N. Yui and J. D. Lewis.
「Nielsen BookData」 より