论文标题
奇异的赫米尔人指标和加塔尼人，藤田和卡瓦玛塔的分解定理
Singular hermitian metrics and the decomposition theorem of Catanese, Fujita, and Kawamata
论文作者
论文摘要
We prove that a torsion-free sheaf $\mathcal F$ endowed with a singular hermitian metric with semi-positive curvature and satisfying the minimal extension property admits a direct-sum decomposition $\mathcal F \simeq \mathcal U \oplus \mathcal A$ where $\mathcal U$ is a hermitian flat bundle and $\mathcal A$ is一般充足的捆。该结果适用于相对多数式捆绑的直接图像$ f_*ω__{x/y}^{\ otimes m} $下的过滤型形态$ f \ colon x \ y $ y $ y $ y $ y $ y $ y $ y $ a $ m \ geq 2 $。这扩展了藤田，卡塔尼 - 卡瓦玛塔和伊瓦的先前结果。
We prove that a torsion-free sheaf $\mathcal F$ endowed with a singular hermitian metric with semi-positive curvature and satisfying the minimal extension property admits a direct-sum decomposition $\mathcal F \simeq \mathcal U \oplus \mathcal A$ where $\mathcal U$ is a hermitian flat bundle and $\mathcal A$ is a generically ample sheaf. The result applies to the case of direct images of relative pluricanonical bundles $f_* ω_{X/Y}^{\otimes m}$ under a surjective morphism $f\colon X \to Y$ of smooth projective varieties with $m\geq 2$. This extends previous results of Fujita, Catanese--Kawamata, and Iwai.
