A Kollár-type vanishing theorem for k-positive vector bundles

IF 1 3区数学 Q1 MATHEMATICS

Forum Mathematicum Pub Date : 2024-03-25 DOI:10.1515/forum-2023-0332

Chen Zhao

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引用次数: 0

Abstract

Given a proper holomorphic surjective morphism f : X → Y

{f:X\rightarrow Y}

between compact Kähler manifolds, and a Nakano semipositive holomorphic vector bundle E on X, we prove Kollár-type vanishing theorems on cohomologies with coefficients in R q ⁢ f ∗ ⁢ ( ω X ⁢ ( E ) ) ⊗ F

{R^{q}f_{\ast}(\omega_{X}(E))\otimes F}

, where F is a k-positive vector bundle on Y. The main inputs in the proof are the deep results on the Nakano semipositivity of the higher direct images due to Berndtsson and Mourougane–Takayama, and an L 2

{L^{2}}

-Dolbeault resolution of the higher direct image sheaf R q ⁢ f ∗ ⁢ ( ω X ⁢ ( E ) )

{R^{q}f_{\ast}(\omega_{X}(E))}

, which is of interest in itself.

查看原文本刊更多论文

k 正向向量束的科拉型消失定理

给定紧凑 Kähler 流形之间的适当全态投射态 f : X → Y {f:X\rightarrow Y} 和 X 上的中野半正全态向量束 E，我们证明了 R q f ∗ ( ω X ( E ) ) 中系数的同调上的 Kollár 型消失定理。 ⊗ F {R^{q}f_{\ast}(\omega_{X}(E))\otimes F} 。证明的主要输入是 Berndtsson 和 Mourougane-Takayama 关于高直达像的中野半实在性的深入结果，以及一个 L 2 {L^{2}} -Dolbeault 解析。高直映像 Sheaf R q f ∗ ( ω X ( E ) ) 的 L 2 {L^{2}} -Dolbeault 解析。 {R^{q}f_{\ast}(\omega_{X}(E))} {R^{q}f_{\ast}(\omega_{X}(E))} ，这本身就很有趣。

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来源期刊

Forum Mathematicum 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Forum Mathematicum is a general mathematics journal, which is devoted to the publication of research articles in all fields of pure and applied mathematics, including mathematical physics. Forum Mathematicum belongs to the top 50 journals in pure and applied mathematics, as measured by citation impact.