On Clifford's theorem for singular curves

Let C be a 2‐connected projective curve either reduced with planar singularities or contained in a smooth algebraic surface and let S be a subcanonical cluster (that is, a zero‐dimensional scheme such that the space H0(C, ℐS KC) contains a generically invertible section). Under some general assumpti...

Full description

Saved in:
Bibliographic Details
Published in:Proceedings of the London Mathematical Society 2014-01, Vol.108 (1), p.225-252
Main Authors: Franciosi, Marco, Tenni, Elisa
Format: Article
Language:English
Citations: 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-c3125-4aa679b840c14866c0c1ea3ee735440e40a5df7a34d955303d5ca9d4242f0ce33
cites
container_end_page 252
container_issue 1
container_start_page 225
container_title Proceedings of the London Mathematical Society
container_volume 108
creator Franciosi, Marco
Tenni, Elisa
description Let C be a 2‐connected projective curve either reduced with planar singularities or contained in a smooth algebraic surface and let S be a subcanonical cluster (that is, a zero‐dimensional scheme such that the space H0(C, ℐS KC) contains a generically invertible section). Under some general assumptions on S or C, we show that h0(C, ℐS KC)⩽pa(C)−½ deg (S) and if equality holds then either S is trivial or C is honestly hyperelliptic or 3‐disconnected. As a corollary, we give a generalization of Clifford's theorem for reduced curves with planar singularities.
doi_str_mv 10.1112/plms/pdt019
format article
fullrecord <record><control><sourceid>wiley_cross</sourceid><recordid>TN_cdi_crossref_primary_10_1112_plms_pdt019</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>PLMS0225</sourcerecordid><originalsourceid>FETCH-LOGICAL-c3125-4aa679b840c14866c0c1ea3ee735440e40a5df7a34d955303d5ca9d4242f0ce33</originalsourceid><addsrcrecordid>eNp9j8FKxDAURYMoWEdX_kB3IlLnveQlnS6lOCpURlDBXYhJqpV2WpIZZf7eDnXt6nDhcOEwdo5wjYh8PrRdnA9uA1gcsARJQcaJ3g5ZAsApU4jymJ3E-AUASgiZsMvVOi3bpq774C5iuvn0ffBdOs40NuuPbWtCarfh28dTdlSbNvqzP87Y6_L2pbzPqtXdQ3lTZVYglxkZo_LifUFgkRZK2ZHeCO9zIYnAExjp6twIcoWUAoST1hSOOPEarBdixq6mXxv6GIOv9RCazoSdRtD7Sr2v1FPlaONk_zSt3_2n6qfq8Rk4l-IXTudV3Q</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>On Clifford's theorem for singular curves</title><source>Wiley</source><creator>Franciosi, Marco ; Tenni, Elisa</creator><creatorcontrib>Franciosi, Marco ; Tenni, Elisa</creatorcontrib><description>Let C be a 2‐connected projective curve either reduced with planar singularities or contained in a smooth algebraic surface and let S be a subcanonical cluster (that is, a zero‐dimensional scheme such that the space H0(C, ℐS KC) contains a generically invertible section). Under some general assumptions on S or C, we show that h0(C, ℐS KC)⩽pa(C)−½ deg (S) and if equality holds then either S is trivial or C is honestly hyperelliptic or 3‐disconnected. As a corollary, we give a generalization of Clifford's theorem for reduced curves with planar singularities.</description><identifier>ISSN: 0024-6115</identifier><identifier>EISSN: 1460-244X</identifier><identifier>DOI: 10.1112/plms/pdt019</identifier><language>eng</language><publisher>Oxford University Press</publisher><ispartof>Proceedings of the London Mathematical Society, 2014-01, Vol.108 (1), p.225-252</ispartof><rights>2014 London Mathematical Society</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c3125-4aa679b840c14866c0c1ea3ee735440e40a5df7a34d955303d5ca9d4242f0ce33</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27922,27923</link.rule.ids></links><search><creatorcontrib>Franciosi, Marco</creatorcontrib><creatorcontrib>Tenni, Elisa</creatorcontrib><title>On Clifford's theorem for singular curves</title><title>Proceedings of the London Mathematical Society</title><description>Let C be a 2‐connected projective curve either reduced with planar singularities or contained in a smooth algebraic surface and let S be a subcanonical cluster (that is, a zero‐dimensional scheme such that the space H0(C, ℐS KC) contains a generically invertible section). Under some general assumptions on S or C, we show that h0(C, ℐS KC)⩽pa(C)−½ deg (S) and if equality holds then either S is trivial or C is honestly hyperelliptic or 3‐disconnected. As a corollary, we give a generalization of Clifford's theorem for reduced curves with planar singularities.</description><issn>0024-6115</issn><issn>1460-244X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNp9j8FKxDAURYMoWEdX_kB3IlLnveQlnS6lOCpURlDBXYhJqpV2WpIZZf7eDnXt6nDhcOEwdo5wjYh8PrRdnA9uA1gcsARJQcaJ3g5ZAsApU4jymJ3E-AUASgiZsMvVOi3bpq774C5iuvn0ffBdOs40NuuPbWtCarfh28dTdlSbNvqzP87Y6_L2pbzPqtXdQ3lTZVYglxkZo_LifUFgkRZK2ZHeCO9zIYnAExjp6twIcoWUAoST1hSOOPEarBdixq6mXxv6GIOv9RCazoSdRtD7Sr2v1FPlaONk_zSt3_2n6qfq8Rk4l-IXTudV3Q</recordid><startdate>201401</startdate><enddate>201401</enddate><creator>Franciosi, Marco</creator><creator>Tenni, Elisa</creator><general>Oxford University Press</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>201401</creationdate><title>On Clifford's theorem for singular curves</title><author>Franciosi, Marco ; Tenni, Elisa</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c3125-4aa679b840c14866c0c1ea3ee735440e40a5df7a34d955303d5ca9d4242f0ce33</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Franciosi, Marco</creatorcontrib><creatorcontrib>Tenni, Elisa</creatorcontrib><collection>CrossRef</collection><jtitle>Proceedings of the London Mathematical Society</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Franciosi, Marco</au><au>Tenni, Elisa</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On Clifford's theorem for singular curves</atitle><jtitle>Proceedings of the London Mathematical Society</jtitle><date>2014-01</date><risdate>2014</risdate><volume>108</volume><issue>1</issue><spage>225</spage><epage>252</epage><pages>225-252</pages><issn>0024-6115</issn><eissn>1460-244X</eissn><abstract>Let C be a 2‐connected projective curve either reduced with planar singularities or contained in a smooth algebraic surface and let S be a subcanonical cluster (that is, a zero‐dimensional scheme such that the space H0(C, ℐS KC) contains a generically invertible section). Under some general assumptions on S or C, we show that h0(C, ℐS KC)⩽pa(C)−½ deg (S) and if equality holds then either S is trivial or C is honestly hyperelliptic or 3‐disconnected. As a corollary, we give a generalization of Clifford's theorem for reduced curves with planar singularities.</abstract><pub>Oxford University Press</pub><doi>10.1112/plms/pdt019</doi><tpages>28</tpages><oa>free_for_read</oa></addata></record>
fulltext fulltext
identifier ISSN: 0024-6115
ispartof Proceedings of the London Mathematical Society, 2014-01, Vol.108 (1), p.225-252
issn 0024-6115
1460-244X
language eng
recordid cdi_crossref_primary_10_1112_plms_pdt019
source Wiley
title On Clifford's theorem for singular curves
url http://sfxeu10.hosted.exlibrisgroup.com/loughborough?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-14T00%3A34%3A48IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-wiley_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=On%20Clifford's%20theorem%20for%20singular%20curves&rft.jtitle=Proceedings%20of%20the%20London%20Mathematical%20Society&rft.au=Franciosi,%20Marco&rft.date=2014-01&rft.volume=108&rft.issue=1&rft.spage=225&rft.epage=252&rft.pages=225-252&rft.issn=0024-6115&rft.eissn=1460-244X&rft_id=info:doi/10.1112/plms/pdt019&rft_dat=%3Cwiley_cross%3EPLMS0225%3C/wiley_cross%3E%3Cgrp_id%3Ecdi_FETCH-LOGICAL-c3125-4aa679b840c14866c0c1ea3ee735440e40a5df7a34d955303d5ca9d4242f0ce33%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