论文标题
降低差异代数和双形的几何形状的降低
Abelian reduction in differential-algebraic and bimeromorphic geometry
论文作者
论文摘要
这里开发了一种差异封闭场和紧凑复合歧管的模型理论的新工具。在这种情况下，显示出一种内部的常数内部类型（分别对射线线）承认，其结合组是Abelian品种的最大图像。稳定理论提供的GALOIS理论框架研究了这种“ Abelian减少”的特性。 然后推导特征零的代数矢量场的生育几何形状的几何后果。特别是（1）表明，如果代数矢量领域的某些笛卡尔力量承认了一个非平凡的有理第一积分，那么第二个权力已经可以，（2）将二维的各向同性代数矢量归类为归类为遵守委员的贵族范围，并将其分类为公正载体等效性。 还获得了这些结果的类似物，也获得了双形几何形状。
A new tool for the model theory of differentially closed fields and of compact complex manifolds is here developed. In such settings, it is shown that a type internal to the field of constants (resp. to the projective line) admits a maximal image whose binding group is an abelian variety. The properties of such "abelian reductions" are investigated in the Galois-theoretic framework provided by stability theory. Several geometric consequences for the birational geometry of algebraic vector fields of characteristic zero are then deduced. In particular, (1) it is shown that if some cartesian power of an algebraic vector field admits a nontrivial rational first integral then already the second power does, (2) two-dimensional isotrivial algebraic vector fields are classified up to birational equivalence, and (3) algebraic vector fields whose finite covers admit no nontrivial factors are studied in arbitrary dimension. Analogues of these results in bimeromorphic geometry are also obtained.
