An introduction to Griffiths' theory of period maps and domains, focused on algebraic, group-theoretic and differential geometric aspects.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
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.
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.
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