Singularities of admissible normal functions

Details Singularities of admissible normal functions Singularities of admissible normal functions

2007-11-06

arxiv.org/abs/0711.0964v2

Mathematics

Algebraic Geometry

23 pages. Added section describing the behavior of singularities under blowing up. This connects our work directly with that o

Scientific paper

In a recent paper, M. Green and P. Griffiths used R. Thomas' works on nodal hypersurfaces to establish the equivalence of the Hodge conjecture and the existence of certain singular admissible normal functions. Inspired by their work, we study normal functions using M. Saito's mixed Hodge modules and prove that the existence of singularities of the type considered by Griffiths and Green is equivalent to the Hodge conjecture. Several of the intermediate results, including a relative version of the weak Lefschetz theorem for perverse sheaves, are of independent interest.

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