1972/03/01 by C. Herbert Clemens, Phillip Griffiths · 14 citations
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Nonlinear Waves and Solitons #Mathematics #Jacobian matrix and determinant #Pure mathematics #Applied mathematics
paper · doi:10.2307/1970801
openalex publication_date 1972/03/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02
Intermediate Jacobians of threefolds 1. Algebraic correspondences and homology relations.2. Families of algebraic curves on a threefold.3. The intermediate Jacobian and its polarizing class.4. The Abel-Jacobi mapping.Part Two.Geometry of cubic hypersurfaces 5.The dual mapping, Lefschetz hypersurfaces.6. Cubic hypersurfaces.7. The variety of lines on a cubic hypersurface.Part Three.The cubic threefold 8.The Fano surface of lines on a cubic threefold, the double point case.9. A topological model for the Fano surface, the non-singular case.10. Distinguished divisors on the Fano surface.Part Four.The intermediate Jacobian of the cubic threefold 11.The Gherardelli-Todd isomorphism.12.The Gauss map and the tangent bundle theorem.13.The "double-six", Torelli, and irrationality theorems.Appendices A. Equivalence relations on the algebraic one-cycles lying on a cubic threefold.B. Unirationality.C. Mumford's theory of Prym varieties and a comment on moduli.