Singularities of admissible normal functions Academic Article

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.

authors

• Pearlstein, Gregory

published proceedings

• Inventiones Mathematicae

author list (cited authors)

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

citation count

• 14

complete list of authors

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

publication date

• September 2009

publisher

• Springer Nature  Publisher

published in

• Inventiones Mathematicae  Journal

keywords

• 49 Mathematical Sciences
• 4902 Mathematical Physics
• 4904 Pure Mathematics

Digital Object Identifier (DOI)

• 10.1007/s00222-009-0191-9

start page

• 599

end page

• 629

volume

• 177

issue

• 3

URL

• http://dx.doi.org/10.1007/s00222-009-0191-9