Patchworking the Log-critical locus of planar curves
We establish a patchworking theorem \`a la Viro for the Log-critical locus of algebraic curves in $(\mathbb{C}^*)^2$. As an application, we prove the existence of projective curves of arbitrary degree with smooth connected Log-critical locus. To prove our patchworking theorem, we study the behaviour...
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| creator | Lang, Lionel Renaudineau, Arthur |
| description | We establish a patchworking theorem \`a la Viro for the Log-critical locus of
algebraic curves in $(\mathbb{C}^*)^2$. As an application, we prove the
existence of projective curves of arbitrary degree with smooth connected
Log-critical locus. To prove our patchworking theorem, we study the behaviour
of Log-inflection points along families of curves defined by Viro polynomials.
In particular, we prove a generalisation of a theorem of Mikhalkin and the
second author on the tropical limit of Log-inflection points. |
| doi_str_mv | 10.48550/arxiv.2103.02576 |
| format | Article |
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algebraic curves in $(\mathbb{C}^*)^2$. As an application, we prove the
existence of projective curves of arbitrary degree with smooth connected
Log-critical locus. To prove our patchworking theorem, we study the behaviour
of Log-inflection points along families of curves defined by Viro polynomials.
In particular, we prove a generalisation of a theorem of Mikhalkin and the
second author on the tropical limit of Log-inflection points.</description><identifier>DOI: 10.48550/arxiv.2103.02576</identifier><language>eng</language><subject>Mathematics - Algebraic Geometry</subject><creationdate>2021-03</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</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/2103.02576$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2103.02576$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Lang, Lionel</creatorcontrib><creatorcontrib>Renaudineau, Arthur</creatorcontrib><title>Patchworking the Log-critical locus of planar curves</title><description>We establish a patchworking theorem \`a la Viro for the Log-critical locus of
algebraic curves in $(\mathbb{C}^*)^2$. As an application, we prove the
existence of projective curves of arbitrary degree with smooth connected
Log-critical locus. To prove our patchworking theorem, we study the behaviour
of Log-inflection points along families of curves defined by Viro polynomials.
In particular, we prove a generalisation of a theorem of Mikhalkin and the
second author on the tropical limit of Log-inflection points.</description><subject>Mathematics - Algebraic Geometry</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzr1uwjAUQGEvHSrKA3TCL5DUv9fOWKGWVopUBvbo2vIFi0CQE2h5e1Ta6WxHH2PPUtTGWytesPzkS62k0LVQ1sEjM2uc4u57KPt83PJpl3g7bKtY8pQj9rwf4nnkA_FTj0csPJ7LJY1P7IGwH9P8vzO2eX_bLD-q9mv1uXxtKwQHVQqAqnEByFk0PpJIFBqJVoMnLT2EgFKACAKQlHONJqmjjc4kRT4YPWOLv-2d3Z1KPmC5dr_87s7XN3uGP4Q</recordid><startdate>20210303</startdate><enddate>20210303</enddate><creator>Lang, Lionel</creator><creator>Renaudineau, Arthur</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20210303</creationdate><title>Patchworking the Log-critical locus of planar curves</title><author>Lang, Lionel ; Renaudineau, Arthur</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a676-eb6a297b6f75a48cf0efb91a5368f3186bba1060b06af27793f13c5c74e2f8b43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Mathematics - Algebraic Geometry</topic><toplevel>online_resources</toplevel><creatorcontrib>Lang, Lionel</creatorcontrib><creatorcontrib>Renaudineau, Arthur</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Lang, Lionel</au><au>Renaudineau, Arthur</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Patchworking the Log-critical locus of planar curves</atitle><date>2021-03-03</date><risdate>2021</risdate><abstract>We establish a patchworking theorem \`a la Viro for the Log-critical locus of
algebraic curves in $(\mathbb{C}^*)^2$. As an application, we prove the
existence of projective curves of arbitrary degree with smooth connected
Log-critical locus. To prove our patchworking theorem, we study the behaviour
of Log-inflection points along families of curves defined by Viro polynomials.
In particular, we prove a generalisation of a theorem of Mikhalkin and the
second author on the tropical limit of Log-inflection points.</abstract><doi>10.48550/arxiv.2103.02576</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Algebraic Geometry |
| title | Patchworking the Log-critical locus of planar curves |
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