{"title":"与四次曲线相关的扎里斯基倍数","authors":"I. Shimada","doi":"10.5427/jsing.2022.24g","DOIUrl":null,"url":null,"abstract":". We investigate Zariski multiples of plane curves Z 1 ,...,Z N such that each Z i is a union of a smooth quartic curve, some of its bitangents, and some of its 4-tangent conics. We show that, for plane curves of this type, the deformation types are equal to the homeomorphism types, and that the number of deformation types grows as O ( d 62 ) when the degree d of the plane curves tends to infinity.","PeriodicalId":44411,"journal":{"name":"Journal of Singularities","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2022-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Zariski multiples associated with quartic curves\",\"authors\":\"I. Shimada\",\"doi\":\"10.5427/jsing.2022.24g\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". We investigate Zariski multiples of plane curves Z 1 ,...,Z N such that each Z i is a union of a smooth quartic curve, some of its bitangents, and some of its 4-tangent conics. We show that, for plane curves of this type, the deformation types are equal to the homeomorphism types, and that the number of deformation types grows as O ( d 62 ) when the degree d of the plane curves tends to infinity.\",\"PeriodicalId\":44411,\"journal\":{\"name\":\"Journal of Singularities\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-09-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Singularities\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5427/jsing.2022.24g\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Singularities","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5427/jsing.2022.24g","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
. We investigate Zariski multiples of plane curves Z 1 ,...,Z N such that each Z i is a union of a smooth quartic curve, some of its bitangents, and some of its 4-tangent conics. We show that, for plane curves of this type, the deformation types are equal to the homeomorphism types, and that the number of deformation types grows as O ( d 62 ) when the degree d of the plane curves tends to infinity.
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