论文标题
旗帜中的表面三倍，包含光滑的圆锥和曲折纤维
Surfaces in the flag threefold containing smooth conics and twistor fibers
论文作者
论文摘要
我们在标志三倍$ \ mathbb {f} $中研究Bidegree $（1,1）$的平滑整体曲线，称为\ textit {smooth {smooth conics}。这项研究的动机是，光滑圆锥的家族包含扭曲器投影$ \ mathbb {f} \ to \ mathbb {cp}^{2} $的纤维集。我们对光滑的表面$ S \ subset \ mathbb {f} $中包含的最大光滑圆锥数量给出了一个界限。然后，我们显示包含大量平滑锥体数量的代数表面的定性特性。最后，我们研究包含许多扭曲纤维的表面。我们表明，唯一平滑的情况是Bidegree $（1,1）$的表面。然后，对于任何整数$ a> 1 $，我们展示了一种构造bidegree $（a，a）$的整体表面的方法，该表面包含无限的许多扭曲器纤维。
We study smooth integral curves of bidegree $(1,1)$, called \textit{smooth conics}, in the flag threefold $\mathbb{F}$. The study is motivated by the fact that the family of smooth conics contains the set of fibers of the twistor projection $\mathbb{F}\to\mathbb{CP}^{2}$. We give a bound on the maximum number of smooth conics contained in a smooth surface $S\subset\mathbb{F}$. Then, we show qualitative properties of algebraic surfaces containing a prescribed number of smooth conics. Lastly, we study surfaces containing infinitely many twistor fibers. We show that the only smooth cases are surfaces of bidegree $(1,1)$. Then, for any integer $a>1$, we exhibit a method to construct an integral surface of bidegree $(a,a)$ containing infinitely many twistor fibers.
