Efficient computation of the branching structure of an algebraic curve
An efficient algorithm for computing the branching structure of a compact Riemann surface defined via an algebraic curve is presented. Generators of the fundamental group of the base of the ramified covering punctured at the discriminant points of the curve are constructed via a minimal spanning tre...
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| creator | Frauendiener, J Klein, C Shramchenko, V |
| description | An efficient algorithm for computing the branching structure of a compact
Riemann surface defined via an algebraic curve is presented. Generators of the
fundamental group of the base of the ramified covering punctured at the
discriminant points of the curve are constructed via a minimal spanning tree of
the discriminant points. This leads to paths of minimal length between the
points, which is important for a later stage where these paths are used as
integration contours to compute periods of the surface. The branching structure
of the surface is obtained by analytically continuing the roots of the equation
defining the algebraic curve along the constructed generators of the
fundamental group. |
| doi_str_mv | 10.48550/arxiv.1108.2038 |
| format | Article |
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Riemann surface defined via an algebraic curve is presented. Generators of the
fundamental group of the base of the ramified covering punctured at the
discriminant points of the curve are constructed via a minimal spanning tree of
the discriminant points. This leads to paths of minimal length between the
points, which is important for a later stage where these paths are used as
integration contours to compute periods of the surface. The branching structure
of the surface is obtained by analytically continuing the roots of the equation
defining the algebraic curve along the constructed generators of the
fundamental group.</description><identifier>DOI: 10.48550/arxiv.1108.2038</identifier><language>eng</language><subject>Computer Science - Computational Geometry ; Mathematics - Algebraic Geometry</subject><creationdate>2011-08</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/1108.2038$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1108.2038$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Frauendiener, J</creatorcontrib><creatorcontrib>Klein, C</creatorcontrib><creatorcontrib>Shramchenko, V</creatorcontrib><title>Efficient computation of the branching structure of an algebraic curve</title><description>An efficient algorithm for computing the branching structure of a compact
Riemann surface defined via an algebraic curve is presented. Generators of the
fundamental group of the base of the ramified covering punctured at the
discriminant points of the curve are constructed via a minimal spanning tree of
the discriminant points. This leads to paths of minimal length between the
points, which is important for a later stage where these paths are used as
integration contours to compute periods of the surface. The branching structure
of the surface is obtained by analytically continuing the roots of the equation
defining the algebraic curve along the constructed generators of the
fundamental group.</description><subject>Computer Science - Computational Geometry</subject><subject>Mathematics - Algebraic Geometry</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj82KwjAURrNxMaj7WQ15gdakN6nJchB_BoTZuC_JbaIBTSWmom9v68zq--DAgUPIJ2elUFKyhUmPcC85Z6qsGKgPsll7HzC4mCl2l2ufTQ5dpJ2n-eSoTSbiKcQjveXUY-6TG5GJ1JyPbqABKfbp7mZk4s355ub_OyWHzfqw2hX73-3P6ntfmFqqQlvfCmmlA18rxgSAtKCqWvNlq-sBAROogaHWwIWqvGyH26IAuRSWVzAlX3_ad0dzTeFi0rMZe5qxB152NkSZ</recordid><startdate>20110809</startdate><enddate>20110809</enddate><creator>Frauendiener, J</creator><creator>Klein, C</creator><creator>Shramchenko, V</creator><scope>AKY</scope><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20110809</creationdate><title>Efficient computation of the branching structure of an algebraic curve</title><author>Frauendiener, J ; Klein, C ; Shramchenko, V</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a658-9bfd45b5e3f68004335b3826917d96d45304c930c9931482f5dc99dc43574b123</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Computer Science - Computational Geometry</topic><topic>Mathematics - Algebraic Geometry</topic><toplevel>online_resources</toplevel><creatorcontrib>Frauendiener, J</creatorcontrib><creatorcontrib>Klein, C</creatorcontrib><creatorcontrib>Shramchenko, V</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Frauendiener, J</au><au>Klein, C</au><au>Shramchenko, V</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Efficient computation of the branching structure of an algebraic curve</atitle><date>2011-08-09</date><risdate>2011</risdate><abstract>An efficient algorithm for computing the branching structure of a compact
Riemann surface defined via an algebraic curve is presented. Generators of the
fundamental group of the base of the ramified covering punctured at the
discriminant points of the curve are constructed via a minimal spanning tree of
the discriminant points. This leads to paths of minimal length between the
points, which is important for a later stage where these paths are used as
integration contours to compute periods of the surface. The branching structure
of the surface is obtained by analytically continuing the roots of the equation
defining the algebraic curve along the constructed generators of the
fundamental group.</abstract><doi>10.48550/arxiv.1108.2038</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Computational Geometry Mathematics - Algebraic Geometry |
| title | Efficient computation of the branching structure of an algebraic curve |
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