Period Mappings and Period Domains

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November 2009



This book discusses the basic properties of period maps and period domains.


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.


'The presentation of the vast material is very lucid and inspiring, methodologically well-planned and utmost user-friendly considering such sophisticated a complex of topics.' Zentralblatt fur Mathematik 'This book, dedicated to Philip Griffiths, provides an excellent introduction to the study of periods of algebraic integrals and their applications to complex algebraic geometry. In addition to the clarity of the presentation and the wealth of information, this book also contains numerous problems which render it ideal for use in a graduate course in Hodge theory.' Mathematical Reviews '... generally more informal and differential-geometric in its approach, which will appeal to many readers. ... the book is a useful introduction to Carlos Simpson's deep analysis of the fundamental groups of compact Kahler manifolds using harmonic maps and Higgs bundles.' Burt Totaro, University of Cambridge
EAN: 9780521814669
ISBN: 0521814669
Untertitel: 'Cambridge Studies in Advanced'. New. Sprache: Englisch.
Erscheinungsdatum: November 2009
Seitenanzahl: 448 Seiten
Format: gebunden
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