Period mappings and period domains
著者
書誌事項
Period mappings and period domains
(Cambridge studies in advanced mathematics, 85)
Cambridge University Press, 2003
- : hardback
大学図書館所蔵 全51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 (p. 415-425) and index
内容説明・目次
内容説明
The period matrix of a curve effectively describes how the complex structure varies; this is Torelli's theorem dating from the beginning of the nineteenth century. In the 1950s during the first revolution of algebraic geometry, attention shifted to higher dimensions and one of the guiding conjectures, the Hodge conjecture, got formulated. In the late 1960s and 1970s Griffiths, in an attempt to solve this conjecture, generalized the classical period matrices introducing period domains and period maps for higher-dimensional manifolds. He then found some unexpected new phenomena for cycles on higher-dimensional algebraic varieties, which were later made much more precise by Clemens, Voisin, Green and others. This 2003 book presents this development starting at the beginning: the elliptic curve. This and subsequent examples (curves of higher genus, double planes) are used to motivate the concepts that play a role in the rest of the book.
目次
- Part I. Basic Theory of the Period Map: 1. Introductory examples
- 2. Cohomology of compact Kahler manifolds
- 3. Holomorphic invariants and cohomology
- 4. Cohomology of manifolds varying in a family
- 5. Period maps looked at infinitesimally
- Part II. The Period Map: Algebraic Methods: 6. Spectral sequences
- 7. Koszul complexes and some applications
- 8. Further applications: Torelli theorems for hypersurfaces
- 9. Normal functions and their applications
- 10. Applications to algebraic cycles: Nori's theorem
- Part III: Differential Geometric Methods: 11. Further differential geometric tools
- 12. Structure of period domains
- 13. Curvature estimates and applications
- 14. Harmonic maps and Hodge theory
- Appendix A. Projective varieties and complex manifolds
- Appendix B. Homology and cohomology
- Appendix C. Vector bundles and Chern classes.
「Nielsen BookData」 より