具有严格 nef 相对反 log 典范除数的代数纤维空间

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-29 DOI:10.1112/jlms.12942

Jie Liu, Wenhao Ou, Juanyong Wang, Xiaokui Yang, Guolei Zhong

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Moreover, when <math>\n <semantics>\n <mrow>\n <mo>dim</mo>\n <mi>X</mi>\n <mo>=</mo>\n <mn>3</mn>\n </mrow>\n <annotation>$\\dim X=3$</annotation>\n </semantics></math> and <math>\n <semantics>\n <mrow>\n <mo>−</mo>\n <mo>(</mo>\n <msub>\n <mi>K</mi>\n <mi>X</mi>\n </msub>\n <mo>+</mo>\n <mi>Δ</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$-(K_X+\\varDelta)$</annotation>\n </semantics></math> is strictly nef, we prove that <math>\n <semantics>\n <mrow>\n <mo>−</mo>\n <mo>(</mo>\n <msub>\n <mi>K</mi>\n <mi>X</mi>\n </msub>\n <mo>+</mo>\n <mi>Δ</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$-(K_X+\\varDelta)$</annotation>\n </semantics></math> is ample, which confirms the singular version of a conjecture by Campana and Peternell for threefolds.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Algebraic fibre spaces with strictly nef relative anti-log canonical divisor\",\"authors\":\"Jie Liu, Wenhao Ou, Juanyong Wang, Xiaokui Yang, Guolei Zhong\",\"doi\":\"10.1112/jlms.12942\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let <math>\\n <semantics>\\n <mrow>\\n <mo>(</mo>\\n <mi>X</mi>\\n <mo>,</mo>\\n <mi>Δ</mi>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$(X,\\\\varDelta)$</annotation>\\n </semantics></math> be a projective klt pair, and <math>\\n <semantics>\\n <mrow>\\n <mi>f</mi>\\n <mo>:</mo>\\n <mi>X</mi>\\n <mo>→</mo>\\n <mi>Y</mi>\\n </mrow>\\n <annotation>$f\\\\colon X\\\\rightarrow Y$</annotation>\\n </semantics></math> a fibration to a smooth projective variety <math>\\n <semantics>\\n <mi>Y</mi>\\n <annotation>$Y$</annotation>\\n </semantics></math> with strictly nef relative anti-log canonical divisor <math>\\n <semantics>\\n <mrow>\\n <mo>−</mo>\\n <mo>(</mo>\\n <msub>\\n <mi>K</mi>\\n <mrow>\\n <mi>X</mi>\\n <mo>/</mo>\\n <mi>Y</mi>\\n </mrow>\\n </msub>\\n <mo>+</mo>\\n <mi>Δ</mi>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$-(K_{X/Y}+\\\\varDelta)$</annotation>\\n </semantics></math>. 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引用次数: 0

摘要

让 ( X , Δ ) $(X,\varDelta)$ 是一个投影 klt 对，并且 f : X → Y $f\colon X\rightarrow Y$ 是一个光滑投影多元 Y $Y$ 的纤度，具有严格 nef 相对反逻辑正则除数 - ( K X / Y + Δ ) $-(K_{X/Y}+\varDelta)$ 。我们证明 f $f$ 是一个具有合理连接纤维的局部琐碎纤维，并且基 Y $Y$ 是一个典型极化双曲流形。特别是，当 Y $Y$ 是一个单点时，我们证明 X $X$ 是有理连接的。此外，当 dim X = 3 $\dim X=3$ 和 - ( K X + Δ ) $-(K_X+\varDelta)$ 是严格 nef 时，我们证明 - ( K X + Δ ) $-(K_X+\varDelta)$ 是充裕的，这证实了坎帕纳和佩特内尔对三维流形的猜想的奇异版本。

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Algebraic fibre spaces with strictly nef relative anti-log canonical divisor

Let $(X, Δ)$ be a projective klt pair, and $f : X \to Y$ a fibration to a smooth projective variety $Y$ with strictly nef relative anti-log canonical divisor $- (K_{X / Y} + Δ)$ . We prove that $f$ is a locally trivial fibration with rationally connected fibres, and the base $Y$ is a canonically polarized hyperbolic manifold. In particular, when $Y$ is a single point, we establish that $X$ is rationally connected. Moreover, when $dim X = 3$ and $- (K_{X} + Δ)$ is strictly nef, we prove that $- (K_{X} + Δ)$ is ample, which confirms the singular version of a conjecture by Campana and Peternell for threefolds.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.