两球产物上的一些Kähler结构

L’Enseignement Mathématique Pub Date : 2017-08-26 DOI:10.4171/LEM/64-1/2-5

J.-F. Lafont, Gangotryi Sorcar, F. Zheng

{"title":"两球产物上的一些Kähler结构","authors":"J.-F. Lafont, Gangotryi Sorcar, F. Zheng","doi":"10.4171/LEM/64-1/2-5","DOIUrl":null,"url":null,"abstract":"We consider a family of K\\\"ahler structures on products of 2-spheres, arising from complex Bott manifolds. These are obtained via iterated $\\mathbb P^1$-bundle constructions, generalizing the classical Hirzebruch surfaces. We show that the resulting K\\\"ahler structures all have identical Chern classes. We construct Bott diagrams, which are rooted forests with an edge labelling by positive integers, and show that these classify these K\\\"ahler structures up to biholomorphism.","PeriodicalId":344085,"journal":{"name":"L’Enseignement Mathématique","volume":"19 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Some Kähler structures on products of 2-spheres\",\"authors\":\"J.-F. Lafont, Gangotryi Sorcar, F. Zheng\",\"doi\":\"10.4171/LEM/64-1/2-5\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a family of K\\\\\\\"ahler structures on products of 2-spheres, arising from complex Bott manifolds. These are obtained via iterated $\\\\mathbb P^1$-bundle constructions, generalizing the classical Hirzebruch surfaces. We show that the resulting K\\\\\\\"ahler structures all have identical Chern classes. We construct Bott diagrams, which are rooted forests with an edge labelling by positive integers, and show that these classify these K\\\\\\\"ahler structures up to biholomorphism.\",\"PeriodicalId\":344085,\"journal\":{\"name\":\"L’Enseignement Mathématique\",\"volume\":\"19 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-08-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"L’Enseignement Mathématique\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/LEM/64-1/2-5\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"L’Enseignement Mathématique","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/LEM/64-1/2-5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 1

摘要

研究了由复数Bott流形引起的2球积上的一类K\ ahler结构。这些是通过迭代$\mathbb P^1$-束构造得到的，推广了经典的Hirzebruch曲面。我们证明了得到的K\ ahler结构都具有相同的chen类。我们构造了以正整数为边缘标记的块状森林的博特图，并证明了这些图将这些K\ ahler结构分类到生物全纯。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Some Kähler structures on products of 2-spheres

We consider a family of K\"ahler structures on products of 2-spheres, arising from complex Bott manifolds. These are obtained via iterated $\mathbb P^1$-bundle constructions, generalizing the classical Hirzebruch surfaces. We show that the resulting K\"ahler structures all have identical Chern classes. We construct Bott diagrams, which are rooted forests with an edge labelling by positive integers, and show that these classify these K\"ahler structures up to biholomorphism.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

L’Enseignement Mathématique

自引率

0.00%

发文量