Computational aspects of gonal maps and radical parametrization of curves

We develop in this article an algorithm that, given a projective curve C , computes a gonal map , that is, a finite morphism from C to P 1 of minimal degree. Our method is based on the computation of scrollar syzygies of canonical curves. We develop an improved version of our algorithm for curves wi...

Full description

Saved in:
Bibliographic Details
Published in:Applicable algebra in engineering, communication and computing communication and computing, 2013-11, Vol.24 (5), p.313-341
Main Authors: Schicho, J., Schreyer, F.-O., Weimann, M.
Format: Article
Language:English
Subjects:
Algebraic Geometry
Artificial Intelligence
Commutative Algebra
Computer Hardware
Computer Science
Mathematics
Original Paper
Symbolic and Algebraic Manipulation
Theory of Computation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
cited_by cdi_FETCH-LOGICAL-c365t-b99ba8bb746710538a50a93769b0f1c74fc2dfc0dfc19efb33b3f1aeea84b7bd3
cites cdi_FETCH-LOGICAL-c365t-b99ba8bb746710538a50a93769b0f1c74fc2dfc0dfc19efb33b3f1aeea84b7bd3
container_end_page 341
container_issue 5
container_start_page 313
container_title Applicable algebra in engineering, communication and computing
container_volume 24
creator Schicho, J.
Schreyer, F.-O.
Weimann, M.
description We develop in this article an algorithm that, given a projective curve C , computes a gonal map , that is, a finite morphism from C to P 1 of minimal degree. Our method is based on the computation of scrollar syzygies of canonical curves. We develop an improved version of our algorithm for curves with a unique gonal map and we discuss a characterization of such curves in terms of Betti numbers. Finally, we derive an efficient algorithm for radical parametrization of curves of gonality ≤ 4 .
doi_str_mv 10.1007/s00200-013-0205-0
format article
fullrecord <record><control><sourceid>hal_cross</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_02137326v1</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>oai_HAL_hal_02137326v1</sourcerecordid><originalsourceid>FETCH-LOGICAL-c365t-b99ba8bb746710538a50a93769b0f1c74fc2dfc0dfc19efb33b3f1aeea84b7bd3</originalsourceid><addsrcrecordid>eNp9kLFOwzAQhi0EEqXwAGxZGQxnO4njsaqAVqrEArN1duySqmkiO60ET4_TIEaG051-_d8NHyH3DB4ZgHyKAByAAhM0HQWFCzJjueAUSs4vyQyUqCjjUl2Tmxh3AFCqXM7Ietm1_XHAoekOuM8w9s4OMet8tj0HLfYxw0OdBawbm4IeA7ZuCM33mRmb9hhOLt6SK4_76O5-95x8vDy_L1d08_a6Xi421IqyGKhRymBljMxLyaAQFRaASshSGfDMytxbXnsLaZhy3ghhhGfoHFa5kaYWc_Iw_f3Eve5D02L40h02erXY6DEDzoQUvDyx1GVT14YuxuD8H8BAj9705E0nb3r0piExfGJi6h62LuhddwzJRfwH-gHhCXDM</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Computational aspects of gonal maps and radical parametrization of curves</title><source>Springer Nature</source><creator>Schicho, J. ; Schreyer, F.-O. ; Weimann, M.</creator><creatorcontrib>Schicho, J. ; Schreyer, F.-O. ; Weimann, M.</creatorcontrib><description>We develop in this article an algorithm that, given a projective curve C , computes a gonal map , that is, a finite morphism from C to P 1 of minimal degree. Our method is based on the computation of scrollar syzygies of canonical curves. We develop an improved version of our algorithm for curves with a unique gonal map and we discuss a characterization of such curves in terms of Betti numbers. Finally, we derive an efficient algorithm for radical parametrization of curves of gonality ≤ 4 .</description><identifier>ISSN: 0938-1279</identifier><identifier>EISSN: 1432-0622</identifier><identifier>DOI: 10.1007/s00200-013-0205-0</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Algebraic Geometry ; Artificial Intelligence ; Commutative Algebra ; Computer Hardware ; Computer Science ; Mathematics ; Original Paper ; Symbolic and Algebraic Manipulation ; Theory of Computation</subject><ispartof>Applicable algebra in engineering, communication and computing, 2013-11, Vol.24 (5), p.313-341</ispartof><rights>Springer-Verlag Berlin Heidelberg 2013</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-c365t-b99ba8bb746710538a50a93769b0f1c74fc2dfc0dfc19efb33b3f1aeea84b7bd3</citedby><cites>FETCH-LOGICAL-c365t-b99ba8bb746710538a50a93769b0f1c74fc2dfc0dfc19efb33b3f1aeea84b7bd3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,777,781,882,27905,27906</link.rule.ids><backlink>$$Uhttps://normandie-univ.hal.science/hal-02137326$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Schicho, J.</creatorcontrib><creatorcontrib>Schreyer, F.-O.</creatorcontrib><creatorcontrib>Weimann, M.</creatorcontrib><title>Computational aspects of gonal maps and radical parametrization of curves</title><title>Applicable algebra in engineering, communication and computing</title><addtitle>AAECC</addtitle><description>We develop in this article an algorithm that, given a projective curve C , computes a gonal map , that is, a finite morphism from C to P 1 of minimal degree. Our method is based on the computation of scrollar syzygies of canonical curves. We develop an improved version of our algorithm for curves with a unique gonal map and we discuss a characterization of such curves in terms of Betti numbers. Finally, we derive an efficient algorithm for radical parametrization of curves of gonality ≤ 4 .</description><subject>Algebraic Geometry</subject><subject>Artificial Intelligence</subject><subject>Commutative Algebra</subject><subject>Computer Hardware</subject><subject>Computer Science</subject><subject>Mathematics</subject><subject>Original Paper</subject><subject>Symbolic and Algebraic Manipulation</subject><subject>Theory of Computation</subject><issn>0938-1279</issn><issn>1432-0622</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNp9kLFOwzAQhi0EEqXwAGxZGQxnO4njsaqAVqrEArN1duySqmkiO60ET4_TIEaG051-_d8NHyH3DB4ZgHyKAByAAhM0HQWFCzJjueAUSs4vyQyUqCjjUl2Tmxh3AFCqXM7Ietm1_XHAoekOuM8w9s4OMet8tj0HLfYxw0OdBawbm4IeA7ZuCM33mRmb9hhOLt6SK4_76O5-95x8vDy_L1d08_a6Xi421IqyGKhRymBljMxLyaAQFRaASshSGfDMytxbXnsLaZhy3ghhhGfoHFa5kaYWc_Iw_f3Eve5D02L40h02erXY6DEDzoQUvDyx1GVT14YuxuD8H8BAj9705E0nb3r0piExfGJi6h62LuhddwzJRfwH-gHhCXDM</recordid><startdate>20131101</startdate><enddate>20131101</enddate><creator>Schicho, J.</creator><creator>Schreyer, F.-O.</creator><creator>Weimann, M.</creator><general>Springer Berlin Heidelberg</general><general>Springer Verlag</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope><scope>VOOES</scope></search><sort><creationdate>20131101</creationdate><title>Computational aspects of gonal maps and radical parametrization of curves</title><author>Schicho, J. ; Schreyer, F.-O. ; Weimann, M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c365t-b99ba8bb746710538a50a93769b0f1c74fc2dfc0dfc19efb33b3f1aeea84b7bd3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Algebraic Geometry</topic><topic>Artificial Intelligence</topic><topic>Commutative Algebra</topic><topic>Computer Hardware</topic><topic>Computer Science</topic><topic>Mathematics</topic><topic>Original Paper</topic><topic>Symbolic and Algebraic Manipulation</topic><topic>Theory of Computation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Schicho, J.</creatorcontrib><creatorcontrib>Schreyer, F.-O.</creatorcontrib><creatorcontrib>Weimann, M.</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>Applicable algebra in engineering, communication and computing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Schicho, J.</au><au>Schreyer, F.-O.</au><au>Weimann, M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Computational aspects of gonal maps and radical parametrization of curves</atitle><jtitle>Applicable algebra in engineering, communication and computing</jtitle><stitle>AAECC</stitle><date>2013-11-01</date><risdate>2013</risdate><volume>24</volume><issue>5</issue><spage>313</spage><epage>341</epage><pages>313-341</pages><issn>0938-1279</issn><eissn>1432-0622</eissn><abstract>We develop in this article an algorithm that, given a projective curve C , computes a gonal map , that is, a finite morphism from C to P 1 of minimal degree. Our method is based on the computation of scrollar syzygies of canonical curves. We develop an improved version of our algorithm for curves with a unique gonal map and we discuss a characterization of such curves in terms of Betti numbers. Finally, we derive an efficient algorithm for radical parametrization of curves of gonality ≤ 4 .</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00200-013-0205-0</doi><tpages>29</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0938-1279
ispartof Applicable algebra in engineering, communication and computing, 2013-11, Vol.24 (5), p.313-341
issn 0938-1279
1432-0622
language eng
recordid cdi_hal_primary_oai_HAL_hal_02137326v1
source Springer Nature
subjects Algebraic Geometry
Artificial Intelligence
Commutative Algebra
Computer Hardware
Computer Science
Mathematics
Original Paper
Symbolic and Algebraic Manipulation
Theory of Computation
title Computational aspects of gonal maps and radical parametrization of curves
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-19T18%3A32%3A47IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-hal_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Computational%20aspects%20of%20gonal%20maps%20and%20radical%20parametrization%20of%20curves&rft.jtitle=Applicable%20algebra%20in%20engineering,%20communication%20and%20computing&rft.au=Schicho,%20J.&rft.date=2013-11-01&rft.volume=24&rft.issue=5&rft.spage=313&rft.epage=341&rft.pages=313-341&rft.issn=0938-1279&rft.eissn=1432-0622&rft_id=info:doi/10.1007/s00200-013-0205-0&rft_dat=%3Chal_cross%3Eoai_HAL_hal_02137326v1%3C/hal_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c365t-b99ba8bb746710538a50a93769b0f1c74fc2dfc0dfc19efb33b3f1aeea84b7bd3%3C/grp_id%3E%3Coa%3E%3C/oa%3E%3Curl%3E%3C/url%3E&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true