b_{2}>12$的法诺4折叠是曲面的乘积

IF 2.6 1区 数学 Q1 MATHEMATICS Inventiones mathematicae Pub Date : 2024-02-05 DOI:10.1007/s00222-024-01236-6
C. Casagrande
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引用次数: 0

摘要

让 \(X\) 是一个光滑、复杂的法诺 4 折叠,\(\rho _{X}\)是它的皮卡尔数。我们证明,如果 \(\rho_{X}>12\),那么 \(X\)就是德尔佩佐曲面的乘积。这个证明依赖于对除法基本收缩 \(f\colon X\to Y\) such that \(\dim f(\operatorname{Exc}(f))=2\) 的仔细研究,以及作者之前关于法诺 4 折叠的工作。特别是,给定上述 \(f\colon X\to Y\), 在合适的假设条件下,我们证明 \(S:=f(\operatorname{Exc}(f))\) 是一个光滑的德尔佩佐曲面,具有 \(-K_{S}=(-K_{Y})_{|S}\)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

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Fano 4-folds with $b_{2}>12$ are products of surfaces

Let \(X\) be a smooth, complex Fano 4-fold, and \(\rho _{X}\) its Picard number. We show that if \(\rho _{X}>12\), then \(X\) is a product of del Pezzo surfaces. The proof relies on a careful study of divisorial elementary contractions \(f\colon X\to Y\) such that \(\dim f(\operatorname{Exc}(f))=2\), together with the author’s previous work on Fano 4-folds. In particular, given \(f\colon X\to Y\) as above, under suitable assumptions we show that \(S:=f(\operatorname{Exc}(f))\) is a smooth del Pezzo surface with \(-K_{S}=(-K_{Y})_{|S}\).

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来源期刊
Inventiones mathematicae
Inventiones mathematicae 数学-数学
CiteScore
5.60
自引率
3.20%
发文量
76
审稿时长
12 months
期刊介绍: This journal is published at frequent intervals to bring out new contributions to mathematics. It is a policy of the journal to publish papers within four months of acceptance. Once a paper is accepted it goes immediately into production and no changes can be made by the author(s).
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