Period mappings and period domains. (Record no. 54509)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 02044 a2200217 4500 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 210325b ||||| |||| 00| 0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781316639566 |
| 082 ## - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 516.35 |
| Item number | CAR |
| 100 ## - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Carlson, James, |
| 245 ## - TITLE STATEMENT | |
| Title | Period mappings and period domains. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 2nd ed. |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Name of publisher, distributor, etc | Cambridge University Press, |
| Date of publication, distribution, etc | 2018. |
| Place of publication, distribution, etc | Cambridge: |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | xiv, 562 p. : ill. ; |
| Other physical details | pb, |
| Dimensions | 24 cm. |
| 365 ## - TRADE PRICE | |
| Price type code | GBP |
| Price amount | 40.99 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE | |
| Bibliography, etc | Includes Biobliography. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | The concept of a period of an elliptic integral goes back to the 18th century. Later Abel, Gauss, Jacobi, Legendre, Weierstrass and others made a systematic study of these integrals. Rephrased in modern terminology, these give a way to encode how the complex structure of a two-torus varies, thereby showing that certain families contain all elliptic curves. Generalizing to higher dimensions resulted in the formulation of the celebrated Hodge conjecture, and in an attempt to solve this, Griffiths generalized the classical notion of period matrix and introduced period maps and period domains which reflect how the complex structure for higher dimensional varieties varies. The basic theory as developed by Griffiths is explained in the first part of the book. Then, in the second part spectral sequences and Koszul complexes are introduced and are used to derive results about cycles on higher dimensional algebraic varieties such as the Noether-Lefschetz theorem and Nori's theorem. Finally, in the third part differential geometric methods are explained leading up to proofs of Arakelov-type theorems, the theorem of the fixed part, the rigidity theorem, and more. Higgs bundles and relations to harmonic maps are discussed, and this leads to striking results such as the fact that compact quotients of certain period domains can never admit a Kahler metric or that certain lattices in classical Lie groups can't occur as the fundamental group of a Kahler manifold. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Geometry |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Mathematics |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Topology |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Source of classification or shelving scheme | Dewey Decimal Classification |
| Item type | Books |
| Withdrawn status | Lost status | Source of classification or shelving scheme | Damaged status | Not for loan | Collection code | Home library | Current library | Shelving location | Date acquired | Source of acquisition | Cost, normal purchase price | Total Checkouts | Full call number | Barcode | Date last seen | Copy number | Cost, replacement price | Koha item type |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Dewey Decimal Classification | General | IIT Gandhinagar | IIT Gandhinagar | General Stacks | 22/03/2021 | Himanshu Books | 0.00 | 516.35 CAR | 030146 | 22/03/2021 | 1 | 0.00 | Books |
