The zero locus of an admissible normal function

Brosnan, Patrick; Pearlstein, Gregory

doi:10.4007/annals.2009.170.883

Cited by 17 publications

(23 citation statements)

References 12 publications

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“…Of course, such normal functions cannot be extended to holomorphic sections; nevertheless, the following is true (see Sect. 4…”

Section: Summary Of the Principal Resultsmentioning

confidence: 97%

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Complex analytic Néron models for arbitrary families of intermediate Jacobians

Schnell

2011

Invent. math.

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Given a family of intermediate Jacobians (for a polarizable variation of integral Hodge structure of odd weight) on a Zariski-open subset of a complex manifold, we construct an analytic space that naturally extends the family. Its two main properties are: (a) the horizontal and holomorphic sections are precisely the admissible normal functions without singularities; (b) the graph of any admissible normal function has an analytic closure inside our space. As a consequence, we obtain a new proof for the zero locus conjecture of M. Green and P. Griffiths. The construction uses filtered D-modules and M. Saito's theory of mixed Hodge modules; it is functorial, and does not require normal crossing or unipotent monodromy assumptions.

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“…Of course, such normal functions cannot be extended to holomorphic sections; nevertheless, the following is true (see Sect. 4…”

Section: Summary Of the Principal Resultsmentioning

confidence: 97%

“…M. Saito has established Conjecture 1.1 for dim X = 1 by this method [35]; an entirely different approach has been pursued by P. Brosnan and G. Pearlstein [4,5], who have announced a full proof in the summer of 2009 [6].…”

Section: Conjecture 11 Let ν Be An Admissible Normal Function On An mentioning

confidence: 99%

Complex analytic Néron models for arbitrary families of intermediate Jacobians

Schnell

2011

Invent. math.

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“…Proof. The fact that Y (F (z),W ) has a well defined limit which commutes with N in the case where (F (z), W ) arises from an admissible normal function is Theorem 3.9 of [3].…”

Section: Variations Of Mixed Hodge Structurementioning

confidence: 95%

Asymptotics of degenerations of mixed Hodge structures

Hayama

Pearlstein

2015

Advances in Mathematics

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“…Lemma 2.20. [Del93,BP06] Let (N ; F, W ) be an admissible nilpotent orbit (in one variable) with limit mixed Hodge structure (F, M ) split over R. Then…”

Section: Admissible Variations On the Punctured Polydiskmentioning

confidence: 99%

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

Brosnan¹,

Pearlstein²

2013

Compositio Math.

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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 2 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 sl 2 -splitting of a real mixed Hodge structure. Corollary 1.3. If S is algebraic then the zero locus of an admissible normal function ν : S → J(H) is an algebraic subvariety of S.

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The zero locus of an admissible normal function

Abstract: We prove that the zero locus of an admissible normal function over an algebraic parameter space S is algebraic in the case where S is a curve.

Cited by 17 publications

References 12 publications

Complex analytic Néron models for arbitrary families of intermediate Jacobians

Complex analytic Néron models for arbitrary families of intermediate Jacobians

Asymptotics of degenerations of mixed Hodge structures

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

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