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Mathematics > Algebraic Geometry

arXiv:0711.0964 (math)
[Submitted on 6 Nov 2007 (v1), last revised 18 Feb 2008 (this version, v2)]

Title:Singularities of admissible normal functions

Authors:Patrick Brosnan (University of British Columbia), Hao Fang (University of Iowa), Zhaohu Nie (Texas A & M), Gregory Pearlstein (Michigan State University)
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Abstract: 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.
Comments: 23 pages. Added section describing the behavior of singularities under blowing up. This connects our work directly with that of Green and Griffiths
Subjects: Algebraic Geometry (math.AG)
MSC classes: 14D07 (Primary); 32S35 (Secondary)
Cite as: arXiv:0711.0964 [math.AG]
  (or arXiv:0711.0964v2 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.0711.0964

Submission history

From: Patrick Brosnan [view email]
[v1] Tue, 6 Nov 2007 20:42:35 UTC (21 KB)
[v2] Mon, 18 Feb 2008 23:18:47 UTC (26 KB)
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