关于具有不变上同调的Kodaira颤振

IF 2 1区数学

Geometry & Topology Pub Date : 2018-11-01 DOI:10.2140/gt.2021.25.2385

Corey Bregman

{"title":"关于具有不变上同调的Kodaira颤振","authors":"Corey Bregman","doi":"10.2140/gt.2021.25.2385","DOIUrl":null,"url":null,"abstract":"A Kodaira fibration is a compact, complex surface admitting a holomorphic submersion onto a complex curve, such that the fibers have nonconstant moduli. We consider Kodaira fibrations X with nontrivial invariant rational cohomology in degree 1, proving that if the dimension of the holomorphic invariants is 1 or 2, then X admits a branch covering over a product of curves inducing an isomorphism on rational cohomology in degree 1. We also study the class of Kodaira fibrations possessing a holomorphic section, and demonstrate that having a section imposes no restriction on possible monodromies.","PeriodicalId":55105,"journal":{"name":"Geometry & Topology","volume":null,"pages":null},"PeriodicalIF":2.0000,"publicationDate":"2018-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"On Kodaira fibrations with invariant cohomology\",\"authors\":\"Corey Bregman\",\"doi\":\"10.2140/gt.2021.25.2385\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A Kodaira fibration is a compact, complex surface admitting a holomorphic submersion onto a complex curve, such that the fibers have nonconstant moduli. We consider Kodaira fibrations X with nontrivial invariant rational cohomology in degree 1, proving that if the dimension of the holomorphic invariants is 1 or 2, then X admits a branch covering over a product of curves inducing an isomorphism on rational cohomology in degree 1. We also study the class of Kodaira fibrations possessing a holomorphic section, and demonstrate that having a section imposes no restriction on possible monodromies.\",\"PeriodicalId\":55105,\"journal\":{\"name\":\"Geometry & Topology\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.0000,\"publicationDate\":\"2018-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Geometry & Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/gt.2021.25.2385\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geometry & Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/gt.2021.25.2385","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 7

摘要

Kodaira纤维是一种致密的复杂表面，允许全纯浸入到复杂曲线上，使得纤维具有非恒定模量。考虑具有1次非平凡不变有理上同构的Kodaira纤曲X，证明了如果全纯不变量的维数为1或2，则X允许分支覆盖在1次有理上同构的曲线乘积上。我们还研究了一类具有全纯截面的Kodaira纤振，并证明了具有全纯截面对可能的单振没有限制。

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

On Kodaira fibrations with invariant cohomology

A Kodaira fibration is a compact, complex surface admitting a holomorphic submersion onto a complex curve, such that the fibers have nonconstant moduli. We consider Kodaira fibrations X with nontrivial invariant rational cohomology in degree 1, proving that if the dimension of the holomorphic invariants is 1 or 2, then X admits a branch covering over a product of curves inducing an isomorphism on rational cohomology in degree 1. We also study the class of Kodaira fibrations possessing a holomorphic section, and demonstrate that having a section imposes no restriction on possible monodromies.

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

Geometry & Topology 数学-数学

自引率

5.00%

发文量

期刊介绍： Geometry and Topology is a fully refereed journal covering all of geometry and topology, broadly understood. G&T is published in electronic and print formats by Mathematical Sciences Publishers. The purpose of Geometry & Topology is the advancement of mathematics. Editors evaluate submitted papers strictly on the basis of scientific merit, without regard to authors" nationality, country of residence, institutional affiliation, sex, ethnic origin, or political views.