论文标题
曲线在加权射击的爆炸中产生极端射线
Curves generating extremal rays in blowups of weighted projective planes
论文作者
论文摘要
我们考虑在加权射击平面的一般点上进行爆炸，更普遍地考虑了PICARD第一的曲面表面。我们对这些爆炸的负曲线进行了统一的构造，以使所有以前已知的家庭都看成是边界案例。该分类由两类上述曲线组成，每个曲线取决于两个参数。这两个类中的每个曲线都与两个类别的其他曲线在代数上相关。这使我们能够归纳地找到其定义方程式。对于分类中的每条曲线，我们考虑了一个爆炸系列，其中曲线定义了有效锥体中的极端阶级。我们将这些爆炸的完整分类为Mori Dream空间和非莫里梦境。我们的方法极大地简化了以前的证据，避免了积极的特征方法和更高的同谋。
We consider blowups at a general point of weighted projective planes and, more generally, of toric surfaces with Picard number one. We give a unifying construction of negative curves on these blowups such that all previously known families appear as boundary cases of this. The classification consists of two classes of said curves, each depending on two parameters. Every curve in these two classes is algebraically related to other curves in both classes; this allows us to find their defining equations inductively. For each curve in our classification, we consider a family of blowups in which the curve defines an extremal class in the effective cone. We give a complete classification of these blowups into Mori Dream Spaces and non-Mori Dream Spaces. Our approach greatly simplifies previous proofs, avoiding positive characteristic methods and higher cohomology.
