论文标题
均匀的坐标环作为常规环的直接汇总
Homogeneous coordinate rings as direct summands of regular rings
论文作者
论文摘要
我们研究了何时可以通过检查均匀坐标环的情况将环作为常规环的直接汇总的问题。我们提出了非常强大的障碍，以表达具有孤立奇异性的分级环作为有限的直接汇总。对于几类示例（del pezzo表面，超曲面），我们给出了一个完整的分类，可以将哪些坐标环表示为直接求和（不一定是有限的），并且这样做回答了Hara关于Quintic del Pezzo的FFRT属性的问题。我们还通过拓扑论点研究了环没有孤立的奇异性的情况：例如，我们给出一个分类，即可以将奇异立方体表面的坐标环写成有限的常规戒指的有限直接汇总。
We study the question of when a ring can be realized as a direct summand of a regular ring by examining the case of homogeneous coordinate rings. We present very strong obstacles to expressing a graded ring with isolated singularity as a finite graded direct summand. For several classes of examples (del Pezzo surfaces, hypersurfaces), we give a complete classification of which coordinate rings can be expressed as direct summands (not necessarily finite), and in doing so answer a question of Hara about the FFRT property of the quintic del Pezzo. We also examine what happens in the case where the ring does not have isolated singularities, through topological arguments: as an example, we give a classification of which coordinate rings of singular cubic surfaces can be written as finite direct summands of regular rings.
