Positivity of the exterior power of the tangent bundles
Positivity of the exterior power of the tangent bundles
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DOI：
10.3792/pjaa.99.015
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发表时间：
2022-08
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影响因子：
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通讯作者：
Kiwamu Watanabe
中科院分区：
文献类型：
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作者：
Kiwamu Watanabe
设$X$是一个复杂的光滑投影变量，使得切线束$\bigwedge^{r} T_X$的外幂对于某些$1\leq r<\dim X$是nef的。我们证明了，在一个可变范围内，$X$是一个阿贝尔变体上的法诺纤维空间。给出了Demailly、Peternell和Schneider等人关于带nef切线束的变元的结构定理和作者关于带nef $\bigwedge^{2} T_X$的变元的结构定理的推广。我们的结果也回答了Li， Ou和Yang对严格nef $\bigwedge^{r} T_X$ when $r<\dim X$的品种提出的问题。
Let $X$ be a complex smooth projective variety such that the exterior power of the tangent bundle $\bigwedge^{r} T_X$ is nef for some $1\leq r<\dim X$. We prove that, up to an \'etale cover, $X$ is a Fano fiber space over an Abelian variety. This gives generalizations of the structure theorem of varieties with nef tangent bundle by Demailly, Peternell and Schneider and that of varieties with nef $\bigwedge^{2} T_X$ by the author. Our result also gives an answer to a question raised by Li, Ou and Yang for varieties with strictly nef $\bigwedge^{r} T_X$ when $r<\dim X$.