论文标题
在一些Fano三倍的积分及其Hilbert线条和圆锥形方案上
On integral points of some Fano Threefolds and their Hilbert schemes of lines and conics
论文作者
论文摘要
令$ x^o = \ mathbb p^3 \ setminus d $其中$ d $是两个四边形的结合，使它们的相交包含光滑的圆锥，或者是光滑的二次表面和两个飞机的结合，或者是平滑的立方体表面$ v $和平面$π$的联合。在所有这些情况下，我们都表明，$ x^o $的一组积分可能是稠密的。我们应用上述结果来证明在某些log-fano或某些log-calabi-yau三倍中，积分点可能是密度的。
Let $X^o=\mathbb P^3\setminus D$ where $D$ is the union of two quadrics such that their intersection contains a smooth conic, or the union of a smooth quadric surface and two planes, or the union of a smooth cubic surface $V$ and a plane $Π$ such that the intersection $V\capΠ$ contains a line. In all these cases we show that the set of integral points of $X^o$ is potentially dense. We apply the above results to prove that integral points are potentially dense in some log-Fano or in some log-Calabi-Yau threefold.
