{"title":"The second syzygy schemes of curves of large degree","authors":"Marian Aprodu, Andrea Bruno, Edoardo Sernesi","doi":"arxiv-2409.11855","DOIUrl":null,"url":null,"abstract":"The present paper is a natural continuation of a previous work where we\nstudied the second syzygy scheme of canonical curves. We find sufficient\nconditions ensuring that the second syzygy scheme of a genus--$g$ curve of\ndegree at least $2g+2$ coincide with the curve. If the property $(N_2)$ is\nsatisfied, the equality is ensured by a more general fact. If $(N_2)$ fails,\nthen the analysis uses the known case of canonical curves.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":"22 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Algebraic Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11855","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
The present paper is a natural continuation of a previous work where we
studied the second syzygy scheme of canonical curves. We find sufficient
conditions ensuring that the second syzygy scheme of a genus--$g$ curve of
degree at least $2g+2$ coincide with the curve. If the property $(N_2)$ is
satisfied, the equality is ensured by a more general fact. If $(N_2)$ fails,
then the analysis uses the known case of canonical curves.
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