Infinitesimal invariant and Massey products
type: Item
instance of: scholarly article
title: Infinitesimal invariant and Massey products
zbMATH Open document ID: 1189.14012
author: Cecilia Rizzi
published in: Manuscripta Mathematica
publication date: 2008-12-02T00:00:00Z
review text: Let \(C\) be a smooth complete connected curve of genus \(g>2\) embedded in its Jacobian variety \(JC\). The Ceresa cycle of \(C\) is the cycle \(Z=C-i(C)\subset CH^{g-1}(JC)\), where \(i=-1\) on \(JC\). It is known that \(Z\) is homologically but not algebraically equivalent to zero for generic \(C\). If \(f:\mathcal C\to S\) is a family of curves of genus \(g>2\) as above and \(\mathcal J\to S\) is its relative Jacobian, then the relative Ceresa cycle \(\mathcal{Z}\in CH^{g-1}(\mathcal J)_{\hom}\) can be considered. The normal function associated to \(\mathcal Z\) is a section \(\nu\) of the relative intermediate Jacobian \(\mathcal J^{g-1}\to S\) defined by \(\nu(s)=AJ_s(Z_s)\), where \(AJ_{s} \) is the higher Abel-Jacobi map. A formula for computing the Griffiths' infinitesimal invariant of \(\nu\) has been given by \textit{A. Collino} and \textit{G. Pirola} [Duke Math. J. 78, 59--88 (1995; Zbl 0846.14016)]. In this paper the author, by means of Collino and Pirola's formula, expresses the Griffiths' infinitesimal invariant of the family in terms of a triple Massey product on a graded differential algebra \(\mathcal A\), defined similarly to the Kodaira-Spencer algebra. As a consequence of this result, it is proved that the differential graded algebra \(\mathcal A\) is not formal.
reviewed by: Michela Artebani
Mathematics Subject Classification ID: 14C25
Mathematics Subject Classification ID: 55S30
Mathematics Subject Classification ID: 14H40
Mathematics Subject Classification ID: 16E45
Mathematics Subject Classification ID: 55S20
zbMATH DE Number: 5377122
zbMATH Keywords: Griffiths' infinitesimal invariant
zbMATH Keywords: Massey product
MaRDI profile type: Publication
full work available at URL: s00229-008-0207-6
OpenAlex ID: W2038078752
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DOI: 10.1007/S00229-008-0207-6
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description: scientific article; zbMATH DE number 5377122