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The Intermediate Jacobian of the Cubic Threefold

1972; Princeton University; Volume: 95; Issue: 2 Linguagem: Inglês

10.2307/1970801

1939-8980

C. Herbert Clemens, Phillip Griffiths,

Nonlinear Waves and Solitons

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.