TY - JOUR
T1 - A transfer principle
T2 - from periods to isoperiodic foliations
AU - Calsamiglia, Gabriel
AU - Deroin, Bertrand
AU - Francaviglia, Stefano
N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
PY - 2023/2/1
Y1 - 2023/2/1
N2 - 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.
AB - 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.
KW - Hodge bundle
KW - Isoperiodic abelian differentials
KW - Isoperiodic foliation
U2 - 10.1007/s00039-023-00627-w
DO - 10.1007/s00039-023-00627-w
M3 - Article
AN - SCOPUS:85147377211
SN - 1016-443X
VL - 33
SP - 57
EP - 169
JO - Geometric and Functional Analysis
JF - Geometric and Functional Analysis
IS - 1
ER -