Universal Deformation of a Curve and a Differential

Universal Deformation of a Curve and a Differential

We construct a universal local deformation (Kuranishi family) for pairs consisting of a compact complex curve and a meromorphic 1-form. Each pair is assumed to be locally planar, a condition which in particular forces the periods of the meromorphic differential to be preserved by local deformations....

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Carberry, Emma, Schmidt, Martin Ulrich
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Algebraic Geometry
Mathematics - Differential Geometry
Online-Zugang:Volltext bestellen
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
container_end_page
container_issue
container_start_page
container_title
container_volume
creator Carberry, Emma
Schmidt, Martin Ulrich
description We construct a universal local deformation (Kuranishi family) for pairs consisting of a compact complex curve and a meromorphic 1-form. Each pair is assumed to be locally planar, a condition which in particular forces the periods of the meromorphic differential to be preserved by local deformations. The hyperelliptic case yields a universal local deformation for the spectral data of integrable systems such as simply-periodic solutions of the KdV equation or of the sinh-Gordon equation (cylinders of constant mean curvature). This is the first of two papers in which we shall develop a deformation theory of the spectral curve data of an integrable system.
doi_str_mv 10.48550/arxiv.2211.11442
format Article
fullrecord <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_2211_11442</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2211_11442</sourcerecordid><originalsourceid>FETCH-LOGICAL-a672-84a867dff63942d87d53aece3da731ff1a14e193aa8f949ad1fea39d057851083</originalsourceid><addsrcrecordid>eNotzstuwjAQhWFvuqhoH6Ar_AJJMx47tpdVoBcJiQ2soxGekSyFBBkalbdvS7s6_-roU-oJmtoG55pnKl95ro0BqAGsNfcK92OeuZxp0CuWqRzpkqdRT6JJd59lZk1j-ulVFuHC4yXT8KDuhIYzP_7vQu1e17vuvdps3z66l01FrTdVsBRan0RajNak4JND4gNjIo8gAgSWISJRkGgjJRAmjKlxPjhoAi7U8u_2pu5PJR-pXPtffX_T4zfRvT6Q</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Universal Deformation of a Curve and a Differential</title><source>arXiv.org</source><creator>Carberry, Emma ; Schmidt, Martin Ulrich</creator><creatorcontrib>Carberry, Emma ; Schmidt, Martin Ulrich</creatorcontrib><description>We construct a universal local deformation (Kuranishi family) for pairs consisting of a compact complex curve and a meromorphic 1-form. Each pair is assumed to be locally planar, a condition which in particular forces the periods of the meromorphic differential to be preserved by local deformations. The hyperelliptic case yields a universal local deformation for the spectral data of integrable systems such as simply-periodic solutions of the KdV equation or of the sinh-Gordon equation (cylinders of constant mean curvature). This is the first of two papers in which we shall develop a deformation theory of the spectral curve data of an integrable system.</description><identifier>DOI: 10.48550/arxiv.2211.11442</identifier><language>eng</language><subject>Mathematics - Algebraic Geometry ; Mathematics - Differential Geometry</subject><creationdate>2022-11</creationdate><rights>http://creativecommons.org/licenses/by/4.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2211.11442$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2211.11442$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Carberry, Emma</creatorcontrib><creatorcontrib>Schmidt, Martin Ulrich</creatorcontrib><title>Universal Deformation of a Curve and a Differential</title><description>We construct a universal local deformation (Kuranishi family) for pairs consisting of a compact complex curve and a meromorphic 1-form. Each pair is assumed to be locally planar, a condition which in particular forces the periods of the meromorphic differential to be preserved by local deformations. The hyperelliptic case yields a universal local deformation for the spectral data of integrable systems such as simply-periodic solutions of the KdV equation or of the sinh-Gordon equation (cylinders of constant mean curvature). This is the first of two papers in which we shall develop a deformation theory of the spectral curve data of an integrable system.</description><subject>Mathematics - Algebraic Geometry</subject><subject>Mathematics - Differential Geometry</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzstuwjAQhWFvuqhoH6Ar_AJJMx47tpdVoBcJiQ2soxGekSyFBBkalbdvS7s6_-roU-oJmtoG55pnKl95ro0BqAGsNfcK92OeuZxp0CuWqRzpkqdRT6JJd59lZk1j-ulVFuHC4yXT8KDuhIYzP_7vQu1e17vuvdps3z66l01FrTdVsBRan0RajNak4JND4gNjIo8gAgSWISJRkGgjJRAmjKlxPjhoAi7U8u_2pu5PJR-pXPtffX_T4zfRvT6Q</recordid><startdate>20221121</startdate><enddate>20221121</enddate><creator>Carberry, Emma</creator><creator>Schmidt, Martin Ulrich</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20221121</creationdate><title>Universal Deformation of a Curve and a Differential</title><author>Carberry, Emma ; Schmidt, Martin Ulrich</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a672-84a867dff63942d87d53aece3da731ff1a14e193aa8f949ad1fea39d057851083</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Mathematics - Algebraic Geometry</topic><topic>Mathematics - Differential Geometry</topic><toplevel>online_resources</toplevel><creatorcontrib>Carberry, Emma</creatorcontrib><creatorcontrib>Schmidt, Martin Ulrich</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Carberry, Emma</au><au>Schmidt, Martin Ulrich</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Universal Deformation of a Curve and a Differential</atitle><date>2022-11-21</date><risdate>2022</risdate><abstract>We construct a universal local deformation (Kuranishi family) for pairs consisting of a compact complex curve and a meromorphic 1-form. Each pair is assumed to be locally planar, a condition which in particular forces the periods of the meromorphic differential to be preserved by local deformations. The hyperelliptic case yields a universal local deformation for the spectral data of integrable systems such as simply-periodic solutions of the KdV equation or of the sinh-Gordon equation (cylinders of constant mean curvature). This is the first of two papers in which we shall develop a deformation theory of the spectral curve data of an integrable system.</abstract><doi>10.48550/arxiv.2211.11442</doi><oa>free_for_read</oa></addata></record>
fulltext fulltext_linktorsrc
identifier DOI: 10.48550/arxiv.2211.11442
ispartof
issn
language eng
recordid cdi_arxiv_primary_2211_11442
source arXiv.org
subjects Mathematics - Algebraic Geometry
Mathematics - Differential Geometry
title Universal Deformation of a Curve and a Differential
url https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-27T12%3A20%3A28IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Universal%20Deformation%20of%20a%20Curve%20and%20a%20Differential&rft.au=Carberry,%20Emma&rft.date=2022-11-21&rft_id=info:doi/10.48550/arxiv.2211.11442&rft_dat=%3Carxiv_GOX%3E2211_11442%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true