Singularities of admissible normal functions: (With an appendix by Najmuddin Fakhruddin)

Patrick Brosnan; Hao Fang; Zhaohu Nie; Gregory Pearlstein

doi:10.1007/s00222-009-0191-9

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Singularities of admissible normal functions: (With an appendix by Najmuddin Fakhruddin)

Journal article

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Singularities of admissible normal functions: (With an appendix by Najmuddin Fakhruddin)

Patrick Brosnan, Hao Fang, Zhaohu Nie and Gregory Pearlstein

Inventiones mathematicae, Vol.177(3), pp.599-629

2009

DOI: 10.1007/s00222-009-0191-9

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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.

Details

Title: Subtitle: Singularities of admissible normal functions: (With an appendix by Najmuddin Fakhruddin)
Creators: Patrick Brosnan
Hao Fang
Zhaohu Nie
Gregory Pearlstein
Resource Type: Journal article
Publication Details: Inventiones mathematicae, Vol.177(3), pp.599-629
DOI: 10.1007/s00222-009-0191-9
ISSN: 0020-9910
eISSN: 1432-1297
Language: English
Date published: 2009
Academic Unit: Mathematics
Record Identifier: 9983985938502771

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