Twistor lines on Nagata threefold

Geometry of lines on certain Moishezon threefolds. I. Explicit description of families of twistor lines

We study real lines on certain Moishezon threefolds which are potentially twistor spaces of 3CP^2. Here, line means a smooth rational curve whose normal bundle is O(1)^2 and the reality implies the invariance under an anti-holomorphic involution on the threefolds. Our threefolds are birational to double coverings of CP^3 branched along singular quartic surfaces. On these threefolds we find families of real lines in explicit form and prove that which families have to be chosen as twistor lines depend on how we take small resolutions of the double covering. This is a first step for determining t…

Double solid twistor spaces II: general case

In this paper we investigate Moishezon twistor spaces which have a structure of double covering over a very simple rational threefold. These spaces can be regarded as a direct generalization of the twistor spaces studied by Poon and Kreussler-Kurke to the case of arbitrary signature. In particular, the branch divisor of the double covering is a cut of the rational threefold by a single quartic hypersurface. A defining equation of the hypersurface is determined in an explicit form. We also show that these twistor spaces interpolate LeBrun twistor spaces and the twistor spaces constructed in mat…

Surfaces in the flag threefold containing smooth conics and twistor fibers

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 surf…

旗三维流形超曲面中的扭量纤维

Twistor fibers in hypersurfaces of the flag threefold

本文研究旗三维流形中双次数(1,d)曲面所含扭量纤维的数量与排列，证明一般位置下不可约曲面最多含d+1条扭量纤维，并在d=2、3时去除了所有一般性假设。

双有理映射下的双曲面族的反向变形

The versal deformation of small resolutions of conic bundles over $\mathbb{P}^1\times\mathbb{P}^1$ with two sections blown down

本文研究了双曲面族的反向变形，揭示了其在 twistor 空间中的结构和变形特性。