Singularities of admissible normal functions Academic Article uri icon

abstract

  • In a recent paper, M. Green and P. Griffiths used R. Thomas' work on nodal hypersurfaces to sketch a proof of the equivalence of the Hodge conjecture and the existence of certain singular admissible normal functions. Inspired by their work, we study normal functions using Morihiko 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. © Springer-Verlag 2009.

author list (cited authors)

  • Brosnan, P., Fang, H., Nie, Z., & Pearlstein, G.

citation count

  • 9

complete list of authors

  • Brosnan, Patrick||Fang, Hao||Nie, Zhaohu||Pearlstein, Gregory

publication date

  • September 2009