论文标题
在全态拟合歧管和退化扭曲变形上，Lagrangian振动的部分
Sections of Lagrangian fibrations on holomorphically symplectic manifolds and degenerate twistorial deformations
论文作者
论文摘要
令$（m，i，ω）$为一个带有holomorphic lagrangian纤维化$π的全态性符号歧管：\; m \ mapsto x $和$η$ a $ x $上的hodge类型（1,1）+（2,0）的封闭形式。我们证明$ω'：=ω+π^*η$再次是一种全态形式的形式，对于另一个复杂的结构$ i'$，它是由$ω'$唯一确定的。复杂结构的相应变形称为“退化扭曲变形”。地图$π$相对于这种新的复杂结构是圆锥形的，$ x $，$π$的纤维保留了与以前相同的复杂结构。令$ s $为$π$的平滑部分。我们证明存在一个退化的扭曲变形$（m，i'，ω'）$，使得$ s $是一个全态部分。
Let $(M,I, Ω)$ be a holomorphically symplectic manifold equipped with a holomorphic Lagrangian fibration $π:\; M \mapsto X$, and $η$ a closed form of Hodge type (1,1)+(2,0) on $X$. We prove that $Ω':=Ω+π^* η$ is again a holomorphically symplectic form, for another complex structure $I'$, which is uniquely determined by $Ω'$. The corresponding deformation of complex structures is called "degenerate twistorial deformation". The map $π$ is holomorphic with respect to this new complex structure, and $X$ and the fibers of $π$ retain the same complex structure as before. Let $s$ be a smooth section of of $π$. We prove that there exists a degenerate twistorial deformation $(M,I', Ω')$ such that $s$ is a holomorphic section.
