{"title":"Images of manifolds with semi-ample anti-canonical divisor","authors":"C. Birkar, Yifei Chen","doi":"10.1090/JAG/662","DOIUrl":null,"url":null,"abstract":"We prove that if f : X → Z is a smooth surjective morphism between projective manifolds and if −KX is semi-ample, then −KZ is also semi-ample. This was conjectured by Fujino and Gongyo. We list several counter-examples to show that this fails without the smoothness assumption on f . We prove the above result by proving some results concerning the moduli divisor of the canonical bundle formula associated to a klt-trivial fibration (X,B)→ Z.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2016-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/JAG/662","citationCount":"10","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebraic Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/JAG/662","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 10
Abstract
We prove that if f : X → Z is a smooth surjective morphism between projective manifolds and if −KX is semi-ample, then −KZ is also semi-ample. This was conjectured by Fujino and Gongyo. We list several counter-examples to show that this fails without the smoothness assumption on f . We prove the above result by proving some results concerning the moduli divisor of the canonical bundle formula associated to a klt-trivial fibration (X,B)→ Z.
期刊介绍：
The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology.
This journal, published quarterly with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.
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