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On the algebraicity of the zero locus of an admissible normal function

Part of: Deformations of analytic structures Families, fibrations

Published online by Cambridge University Press:  28 August 2013

Patrick Brosnan  and
Gregory Pearlstein
Patrick Brosnan
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742, USA email pbrosnan@umd.edu
Gregory Pearlstein
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843, USA email gpearl@math.tamu.edu
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Abstract

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We show that the zero locus of an admissible normal function on a smooth complex algebraic variety is algebraic. In Part II of the paper, which is an appendix, we compute the Tannakian Galois group of the category of one-variable admissible real nilpotent orbits with split limit. We then use the answer to recover an unpublished theorem of Deligne, which characterizes the ${\mathrm{sl} }_{2} $-splitting of a real mixed Hodge structure.

Keywords

normal functionsHodge theory

MSC classification

Secondary: 32G20: Period matrices, variation of Hodge structure; degenerations 14D07: Variation of Hodge structures 14D05: Structure of families (Picard-Lefschetz, monodromy, etc.)
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 11 , November 2013 , pp. 1913 - 1962
Copyright
© The Author(s) 2013 

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