AI 中文总结
本文针对双有理几何中构造开簇对数典范紧化的核心问题，提出利用正几何典范形式获取对数典范模型显式坐标的方法，并将其应用于超平面排列补集等三类具体对象。
AI 中文摘要
构造开簇的对数典范紧化是双有理几何中的核心问题，通常难以找到自然坐标系并得到这些模型的方程。本文证明，对于一大类簇，对数典范模型的显式坐标由正几何的典范形式提供，并利用这一点计算这些模型的方程。该理论适用于超平面排列的补集、去掉直线的三次曲面，以及带标记的三次 del Pezzo 曲面的模空间。
英文摘要
Constructing log canonical compactifications of open varieties is a central problem in birational geometry. Finding a natural coordinate system and obtaining the equations of these models is difficult in general. We show that for a large class of varieties explicit coordinates for the log canonical model are provided by canonical forms of positive geometries, and use this to compute the equations of these models. Our theory applies, for instance, to complements of hyperplane arrangements, cubic surfaces with lines removed, and the moduli space of marked cubic del Pezzo surfaces.
Comments23 pages, 3 figures, comments welcome!
