Singularities of admissible normal functions |
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| Authors: | Patrick Brosnan Hao Fang Zhaohu Nie Gregory Pearlstein |
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| Institution: | (1) Department of Mathematics, The University of British Columbia, 1984 Mathematics Road, Vancouver, BC, Canada, V6T 1Z2;(2) Department of Mathematics, College of Liberal Arts & Sciences, University of Iowa, 14 MLH, Iowa City, IA 52242, USA;(3) Department of Mathematics, Penn State Altoona, 3000 Ivyside Park, Altoona, PA 16601, USA;(4) Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA |
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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.
P. Brosnan’s research was supported in part by an NSERC discovery grant.
H. Fang’s research was supported in part by NSF grant number DMS 0606721.
G. Pearlstein’s research was supported in part by NSF grant number DMS 0703956.
N. Fakhruddin
School of Mathematics, Tata Institue of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
e-mail: naf@math.tifr.res.in |
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