论文标题
calabi-yau三倍的理性曲线和严格的nef除数
Rational curves and strictly nef divisors on Calabi--Yau threefolds
论文作者
论文摘要
我们给出一个Nef Divisor $ d $的标准，以在calabi-yau三倍$ x $上进行半iame，当$ d^3 = 0 = 0 = c_2（x）\ cdot d $和$ c_3（x）\ neq 0 $。作为一个直接的结果，我们表明，如果$ d $是严格的nef，而$ν（d）\ neq 1 $，则$ d $很足够；我们还表明，如果存在一个nef非样品除法$ d $，$ d \ not \ equiv 0 $，则$ x $包含一个理性曲线，当它的拓扑欧拉特性不是$ 0 $。
We give a criterion for a nef divisor $D$ to be semiample on a Calabi--Yau threefold $X$ when $D^3=0=c_2(X)\cdot D$ and $c_3(X)\neq 0$. As a direct consequence, we show that on such a variety $X$, if $D$ is strictly nef and $ν(D)\neq 1$, then $D$ is ample; we also show that if there exists a nef non-ample divisor $D$ with $D\not\equiv 0$, then $X$ contains a rational curve when its topological Euler characteristic is not $0$.
