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A Survey of the Hodge Conjecture: Second Edition
About this Title
James D. Lewis, University of Alberta, Edmonton, AB, Canada and B. Brent Gordon, University of Oklahoma, Norman, OK
Publication: CRM Monograph Series
Publication Year:
1999; Volume 10
ISBNs: 978-1-4704-2852-5 (print); 978-1-4704-3856-2 (online)
DOI: https://doi.org/10.1090/crmm/010
MathSciNet review: MR1683216
MSC: Primary 14C30; Secondary 32J25
ReadershipTable of Contents
Front/Back Matter
Chapters
- Complex manifolds
- Vector bundles
- Kähler manifolds
- Line bundles
- The Lefschetz (1,1) theorem
- The Lefschetz (1,1) theorem revisited
- Formulation of the general Hodge conjecture
- Chern class theory
- Cohomology of complete intersections
- The Hodge theorem
- Analytic and topological necessities of the Kähler condition
- Intermediate Jacobians
- Various approaches to the Hodge conjecture for varieties with well understood geometric structure
- The approach to the Hodge conjecture via normal functions
- Hodge theory and Chow groups
- Appendix A. Results and formulations in the singular case
- Appendix B. A survey of the Hodge conjecture for abelian varieties