James Carlson (University of Utah), Stefan Muller-Stach (Germany Johannes Gutenberg Universitat Mainz), Chris Peters

Period Mappings and Period Domains

• Gebundenes Buch

Produktbeschreibung

This up-to-date introduction to Griffiths' theory of period maps and period domains focusses on algebraic, group-theoretic and differential geometric aspects. The second edition has been thoroughly revised and now includes a new third section covering recent and important new developments in the field.

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Produktdetails

• Cambridge Studies in Advanced Mathematics
• Verlag: Cambridge University Press
• 2 Revised edition
• Seitenzahl: 578
• Erscheinungstermin: 27. Juli 2017
• Englisch
• Abmessung: 235mm x 157mm x 38mm
• Gewicht: 1020g
• ISBN-13: 9781108422628
• ISBN-10: 1108422624
• Artikelnr.: 48955776

Autorenporträt

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.

Inhaltsangabe

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.