{"title":"k3曲面上的尖曲线是有理椭圆曲面的双重覆盖","authors":"Jiryo Komeda, Makiko Mase","doi":"10.21099/tkbjm/20234701065","DOIUrl":null,"url":null,"abstract":"This article is a continuation of [4] in a way. We construct pointed curves on the K3 surfaces treated in [1] which are double covers of rational elliptic surfaces. In some cases we calculate the Weierstrass semigroups of the pointed curves. These pointed curves are the first examples on K3 surfaces that are double covers of rational elliptic surfaces such that we can calculate the Weierstrass semigroups. Moreover, we give bi-elliptic curves of genus 9 or 10 on some such K3 surfaces.","PeriodicalId":44321,"journal":{"name":"Tsukuba Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"POINTED CURVES ON K3 SURFACES WHICH ARE DOUBLE COVERS OF RATIONAL ELLIPTIC SURFACES\",\"authors\":\"Jiryo Komeda, Makiko Mase\",\"doi\":\"10.21099/tkbjm/20234701065\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This article is a continuation of [4] in a way. We construct pointed curves on the K3 surfaces treated in [1] which are double covers of rational elliptic surfaces. In some cases we calculate the Weierstrass semigroups of the pointed curves. These pointed curves are the first examples on K3 surfaces that are double covers of rational elliptic surfaces such that we can calculate the Weierstrass semigroups. Moreover, we give bi-elliptic curves of genus 9 or 10 on some such K3 surfaces.\",\"PeriodicalId\":44321,\"journal\":{\"name\":\"Tsukuba Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Tsukuba Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.21099/tkbjm/20234701065\",\"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":"Tsukuba Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21099/tkbjm/20234701065","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
POINTED CURVES ON K3 SURFACES WHICH ARE DOUBLE COVERS OF RATIONAL ELLIPTIC SURFACES
This article is a continuation of [4] in a way. We construct pointed curves on the K3 surfaces treated in [1] which are double covers of rational elliptic surfaces. In some cases we calculate the Weierstrass semigroups of the pointed curves. These pointed curves are the first examples on K3 surfaces that are double covers of rational elliptic surfaces such that we can calculate the Weierstrass semigroups. Moreover, we give bi-elliptic curves of genus 9 or 10 on some such K3 surfaces.
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