Period Mappings and Period Domains

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Sprache: Englisch

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Beschreibung

This up-to-date introduction to Griffiths' theory of period maps and period domains focusses on algebraic, group-theoretic and differential geometric aspects. Starting with an explanation of Griffiths' basic theory, the authors go on to introduce spectral sequences and Koszul complexes that are used to derive results about cycles on higher-dimensional algebraic varieties such as the Noether-Lefschetz theorem and Nori's theorem. They explain differential geometric methods, leading up to proofs of Arakelov-type theorems, the theorem of the fixed part and the rigidity theorem. They also use Higgs bundles and harmonic maps to prove the striking result that not all compact quotients of period domains are Kähler. This thoroughly revised second edition includes a new third part covering important recent developments, in which the group-theoretic approach to Hodge structures is explained, leading to Mumford-Tate groups and their associated domains, the Mumford-Tate varieties and generalizations of Shimura varieties.

Über den Autor

James Carlson is Professor Emeritus at the University of Utah. From 2003 to 2012, he was president of the Clay Mathematics Institute, New Hampshire. Most of Carlson's research is in the area of Hodge theory.

Inhaltsverzeichnis

Part I. Basic Theory: 1. Introductory examples; 2. Cohomology of compact Kähler manifolds; 3. Holomorphic invariants and cohomology; 4. Cohomology of manifolds varying in a family; 5. Period maps looked at infinitesimally; Part II. Algebraic Methods: 6. Spectral sequences; 7. Koszul complexes and some applications; 8. Torelli theorems; 9. Normal functions and their applications; 10. Applications to algebraic cycles: Nori's theorem; Part III. Differential Geometric Aspects: 11. Further differential geometric tools; 12. Structure of period domains; 13. Curvature estimates and applications; 14. Harmonic maps and Hodge theory; Part IV. Additional Topics: 15. Hodge structures and algebraic groups; 16. Mumford-Tate domains; 17. Hodge loci and special subvarieties; Appendix A. Projective varieties and complex manifolds; Appendix B. Homology and cohomology; Appendix C. Vector bundles and Chern classes; Appendix D. Lie groups and algebraic groups; References; Index.

Details

Erscheinungsjahr:	2017
Fachbereich:	Geometrie
Genre:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	Kartoniert / Broschiert
ISBN-13:	9781316639566
ISBN-10:	1316639568
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Carlson, James Müller-Stach, Stefan Peters, Chris
Hersteller:	Cambridge University Press
Verantwortliche Person für die EU:	Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße:	229 x 152 x 34 mm
Von/Mit:	James Carlson (u. a.)
Erscheinungsdatum:	24.08.2017
Gewicht:	0,927 kg