{"title":"大等级曲线的第二协同方案","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":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":null,\"pages\":null},\"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}","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}
The second syzygy schemes of curves of large degree
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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