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Mathematics Colloquium


Date:  Tuesday, December 12, 2006

Title:  Algebraic Cycles and Singularities of Normal Functions

Abstract:  It has been known for some time that Hodge classes give normal functions, but the usefulness of this result in constructing algebraic cycles has been severely limited due to the failure of Jacobi inversions in higher dimensions. In a joint work with Mark Green, we make the point that the singularities of normal functions - which in the locus where they cease to be "normal" in Poincare's original terminology - are of considerable significance. In addition to having an interesting and novel algebro-geometric structure, we prove that, in a precise sense, the singular locus gives the equations of "duals" of Hodge classes. As a consequence, the Hodge conjecture is equivalent to the singular locus being non-empty for sufficiently ample hypersurface sections.

Speaker:  Phillip Griffiths
Institution:  IAS


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