论文标题
在Kodaira Codimension的品种上，无处消失的全态单形式
Nowhere vanishing holomorphic one-forms on varieties of Kodaira codimension one
论文作者
论文摘要
基于Popa和Schnell的复杂品种的全体形态1形式的零态零，我们研究了Kodaira Dimension $ n-1 $的holomorphic 1forms。我们表明，复杂的最小光滑的投影品种$ x $的kodaira dimension $κ（x）= \ dim x-1 $在且仅当从$ x $到椭圆曲线的平滑形态时，且仅当具有光滑的形态时，holomorphic 1型不为零。此外，对于一般光滑的投影品种（不一定是最小）$ x $的kodaira codimension One，我们给出了$ x $的结构定理，因为$ x $允许holomorphic 1型，而无需零。
Based on the celebrated result on zeros of holomorphic 1-forms on complex varieties of general type by Popa and Schnell, we study holomorphic 1-forms on $n$-dimensional varieties of Kodaira dimension $n-1$. We show that a complex minimal smooth projective variety $X$ of Kodaira dimension $κ(X)=\dim X-1$ admits a holomorphic 1-form without zero if and only if there is a smooth morphism from $X$ to an elliptic curve. Furthermore, for a general smooth projective variety (not necessarily minimal) $X$ of Kodaira codimension one, we give a structure theorem for $X$ given that $X$ admits a holomorphic 1-form without zero.
