A transfer principle: from periods to isoperiodic foliations

We classify the possible closures of leaves of the isoperiodic foliation defined on the Hodge bundle over the moduli space of genus g ≥ 2 curves and prove that the foliation is ergodic on those sets. The results derive from the connectedness properties of the fibers of the period map defined on the...

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Bibliographic Details
Published inGeometric and functional analysis Vol. 33; no. 1; pp. 57 - 169
Main Authors Calsamiglia, Gabriel, Deroin, Bertrand, Francaviglia, Stefano
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.02.2023
Springer Nature B.V
Springer Verlag
Subjects
Analysis
Curves
Mathematics
Mathematics and Statistics
Set theory
Topology
Hodge bundle
14H15
57M50
30F30
53A30
Isoperiodic foliation
32G13
Isoperiodic abelian differentials
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Summary:We classify the possible closures of leaves of the isoperiodic foliation defined on the Hodge bundle over the moduli space of genus g ≥ 2 curves and prove that the foliation is ergodic on those sets. The results derive from the connectedness properties of the fibers of the period map defined on the Torelli cover of the moduli space. Some consequences on the topology of Hurwitz spaces of primitive branched coverings over elliptic curves are also obtained. To prove the results we develop the theory of augmented Torelli space, the branched Torelli cover of the Deligne–Mumford compactification of the moduli space of curves.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-023-00627-w