Period Mappings and Period Domains

ISBN-13: 9781316639566 / Angielski / Miękka / 2017 / 576 str.

James Carlson; Stefan Muller-Stach; Chris Peters

Opis

An introduction to Griffiths' theory of period maps and domains, focused on algebraic, group-theoretic and differential geometric aspects.

Recenzje

'This monograph provides an excellent introduction to Hodge theory and its applications to complex algebraic geometry.' Gregory Pearlstein, Nieuw Archief voor Weskunde

Spis treści

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.