SEARCH Events
Event Title: OR
Speaker Last Name:    OR
Year: (yyyy)


Mathematics Colloquium

EVENT DETAIL

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

 

Back to current Colloquium List
Back to UM Math seminars page

   

Department of Mathematics   |   2074 East Hall   |  530 Church Street  
Ann Arbor, MI 48109-1043
Phone: 734.764-0335   |   Fax: 734.763-0937

The page last modified
Site errors should be directed to math-webmaster@umich.edu