{"title":"在Hirzebruch曲面上最大限度地弯曲实三角形曲线","authors":"V. Zvonilov","doi":"10.1090/conm/772/15498","DOIUrl":null,"url":null,"abstract":"In 2014 A. Degtyarev, I. Itenberg, and the author gave a description, up to fiberwise equivariant deformations, of maximally inflected real trigonal curves of type I (over a base \n\n \n B\n B\n \n\n of an arbitrary genus) in terms of the combinatorics of sufficiently simple graphs and for \n\n \n \n B\n =\n \n \n P\n \n 1\n \n \n B=\\mathbb {P}^1\n \n\n obtained a complete classification of such curves. In this paper, the mentioned results are extended to maximally inflected real trigonal curves of type II over \n\n \n \n B\n =\n \n \n P\n \n 1\n \n \n B=\\mathbb {P}^1\n \n\n.","PeriodicalId":296603,"journal":{"name":"Topology, Geometry, and Dynamics","volume":"159 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-02-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Maximally inflected real trigonal curves on Hirzebruch surfaces\",\"authors\":\"V. Zvonilov\",\"doi\":\"10.1090/conm/772/15498\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In 2014 A. Degtyarev, I. Itenberg, and the author gave a description, up to fiberwise equivariant deformations, of maximally inflected real trigonal curves of type I (over a base \\n\\n \\n B\\n B\\n \\n\\n of an arbitrary genus) in terms of the combinatorics of sufficiently simple graphs and for \\n\\n \\n \\n B\\n =\\n \\n \\n P\\n \\n 1\\n \\n \\n B=\\\\mathbb {P}^1\\n \\n\\n obtained a complete classification of such curves. In this paper, the mentioned results are extended to maximally inflected real trigonal curves of type II over \\n\\n \\n \\n B\\n =\\n \\n \\n P\\n \\n 1\\n \\n \\n B=\\\\mathbb {P}^1\\n \\n\\n.\",\"PeriodicalId\":296603,\"journal\":{\"name\":\"Topology, Geometry, and Dynamics\",\"volume\":\"159 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-02-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topology, Geometry, and Dynamics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/conm/772/15498\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topology, Geometry, and Dynamics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/conm/772/15498","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
在2014年A。Degtyarev, I. Itenberg和作者用足够简单图的组合学描述了I型(任意属B B上)的最大弯曲实三角曲线的纤维等变变形，并对B= P 1 B=\mathbb {P}^1给出了这类曲线的完全分类。本文将上述结果推广到B= P 1 B=\mathbb {P}^1上II型最大弯曲实三角曲线。
Maximally inflected real trigonal curves on Hirzebruch surfaces
In 2014 A. Degtyarev, I. Itenberg, and the author gave a description, up to fiberwise equivariant deformations, of maximally inflected real trigonal curves of type I (over a base
B
B
of an arbitrary genus) in terms of the combinatorics of sufficiently simple graphs and for
B
=
P
1
B=\mathbb {P}^1
obtained a complete classification of such curves. In this paper, the mentioned results are extended to maximally inflected real trigonal curves of type II over
B
=
P
1
B=\mathbb {P}^1
.
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