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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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| Published in: | Geometric and functional analysis 2023-02, Vol.33 (1), p.57-169 |
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| Main Authors: | , , |
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| container_end_page | 169 |
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| container_start_page | 57 |
| container_title | Geometric and functional analysis |
| container_volume | 33 |
| creator | Calsamiglia, Gabriel Deroin, Bertrand Francaviglia, Stefano |
| description | 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. |
| doi_str_mv | 10.1007/s00039-023-00627-w |
| format | article |
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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.</description><identifier>ISSN: 1016-443X</identifier><identifier>EISSN: 1420-8970</identifier><identifier>DOI: 10.1007/s00039-023-00627-w</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Analysis ; Curves ; Mathematics ; Mathematics and Statistics ; Set theory ; Topology</subject><ispartof>Geometric and functional analysis, 2023-02, Vol.33 (1), p.57-169</ispartof><rights>The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c397t-3a6d34ecd3f27fff41da04179bacfcf6695a56b92edd888d8d42dd9e6c377e433</citedby><cites>FETCH-LOGICAL-c397t-3a6d34ecd3f27fff41da04179bacfcf6695a56b92edd888d8d42dd9e6c377e433</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,776,780,881,27903,27904</link.rule.ids><backlink>$$Uhttps://hal.science/hal-03060643$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Calsamiglia, Gabriel</creatorcontrib><creatorcontrib>Deroin, Bertrand</creatorcontrib><creatorcontrib>Francaviglia, Stefano</creatorcontrib><title>A transfer principle: from periods to isoperiodic foliations</title><title>Geometric and functional analysis</title><addtitle>Geom. Funct. Anal</addtitle><description>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.</description><subject>Analysis</subject><subject>Curves</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Set theory</subject><subject>Topology</subject><issn>1016-443X</issn><issn>1420-8970</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kMtKAzEUhoMoWKsv4GrAlYvoyWWSGXFTijcouFFwF9JcdMp0MiZTi29v6ojuXJ2c8P0_hw-hUwIXBEBeJgBgNQbKMICgEm_30IRwCriqJeznNxCBOWcvh-gopVXGy5KXE3Q9K4aou-RdLPrYdKbpW3dV-BjWRe9iE2wqhlA0KYxbYwof2kYPTejSMTrwuk3u5GdO0fPtzdP8Hi8e7x7mswU2rJYDZlpYxp2xzFPpvefEauBE1kttvPFC1KUuxbKmztqqqmxlObW2dsIwKR1nbIrOx9433ap85VrHTxV0o-5nC7X7AwYCBGcfJLNnI9vH8L5xaVCrsIldPk9RWfFK8qwlU3SkTAwpRed_awmonVE1GlXZqPo2qrY5xMZQ2pl6dfGv-p_UFz9oeTQ</recordid><startdate>20230201</startdate><enddate>20230201</enddate><creator>Calsamiglia, Gabriel</creator><creator>Deroin, Bertrand</creator><creator>Francaviglia, Stefano</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><general>Springer Verlag</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><scope>VOOES</scope></search><sort><creationdate>20230201</creationdate><title>A transfer principle: from periods to isoperiodic foliations</title><author>Calsamiglia, Gabriel ; Deroin, Bertrand ; Francaviglia, Stefano</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c397t-3a6d34ecd3f27fff41da04179bacfcf6695a56b92edd888d8d42dd9e6c377e433</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Analysis</topic><topic>Curves</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Set theory</topic><topic>Topology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Calsamiglia, Gabriel</creatorcontrib><creatorcontrib>Deroin, Bertrand</creatorcontrib><creatorcontrib>Francaviglia, Stefano</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Geometric and functional analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Calsamiglia, Gabriel</au><au>Deroin, Bertrand</au><au>Francaviglia, Stefano</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A transfer principle: from periods to isoperiodic foliations</atitle><jtitle>Geometric and functional analysis</jtitle><stitle>Geom. Funct. Anal</stitle><date>2023-02-01</date><risdate>2023</risdate><volume>33</volume><issue>1</issue><spage>57</spage><epage>169</epage><pages>57-169</pages><issn>1016-443X</issn><eissn>1420-8970</eissn><abstract>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.</abstract><cop>Cham</cop><pub>Springer International Publishing</pub><doi>10.1007/s00039-023-00627-w</doi><tpages>113</tpages><oa>free_for_read</oa></addata></record> |
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| language | eng |
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| subjects | Analysis Curves Mathematics Mathematics and Statistics Set theory Topology |
| title | A transfer principle: from periods to isoperiodic foliations |
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