论文标题
切线束的第二个外部力量的积极性
Positivity of the second exterior power of the tangent bundles
论文作者
论文摘要
让$ x $成为一个光滑的复杂投影品种，使用nef $ \ bigwedge^2 t_x $和$ \ dim x \ geq 3 $。我们证明，直到有限的étale覆盖$ \ tilde {x} \ to x $，Albanese Map $ \ tilde {x} \ to {\ rm alb}（\ rm alb}（\ tilde {x}）$是本地纤维的纤维，其纤维是一个fibers fibers fibers fibers fiber to smootheede to smooth y to Smplace pano $ $ f $ f $ f $ f nef $ f nef $ f nef $ f nef $ f。作为双层产品，我们看到$ t_x $是nef，或者$ x $是Fano品种。此外，我们研究了$ k_x $ - 阴性极值$φ的收缩：x \ to y $。特别是，我们证明$ x $是同构成投影空间的同构，如果$φ$是Birational类型的。我们还证明，如果$φ$是纤维类型，则$φ$是一种平稳的形态。结果，我们使用nef $ \ bigwedge^2 t_x $提供了一个结构定理。
Let $X$ be a smooth complex projective variety with nef $\bigwedge^2 T_X$ and $\dim X \geq 3$. We prove that, up to a finite étale cover $\tilde{X} \to X$, the Albanese map $\tilde{X} \to {\rm Alb}(\tilde{X})$ is a locally trivial fibration whose fibers are isomorphic to a smooth Fano variety $F$ with nef $\bigwedge^2 T_F$. As a bi-product, we see that either $T_X$ is nef or $X$ is a Fano variety. Moreover we study a contraction of a $K_X$-negative extremal ray $φ: X \to Y$. In particular, we prove that $X$ is isomorphic to the blow-up of a projective space at a point if $φ$ is of birational type. We also prove that $φ$ is a smooth morphism if $φ$ is of fiber type. As a consequence, we give a structure theorem of varieties with nef $\bigwedge^2 T_X$.
