论文标题
在循环强的特殊收集线束上
On cyclic strong exceptional collections of line bundles on surfaces
论文作者
论文摘要
我们研究表面上的线条束的特殊集合。我们证明，在理性表面上，任何完整的循环强度集合都在L.Hille和M.Perling的意义上是一种增强。我们发现，对于弱的del pezzo表面上的线束的集合，我们发现了异常的简单几何标准（强大的异常，循环强的异常性）。结果，我们对光滑的投影表面进行了分类，并承认了完整的循环强大的线条束集合。另外，我们提供了一个弱Del Pezzo 2度的弱Del Pezzo表面的示例，并提供了完整的强大线条束集合，并非来自增强，从而回答了Hille和Perling的问题。
We study exceptional collections of line bundles on surfaces. We prove that any full cyclic strong exceptional collection of line bundles on a rational surface is an augmentation in the sense of L.Hille and M.Perling. We find simple geometric criteria of exceptionality (strong exceptionality, cyclic strong exceptionality) for collections of line bundles on weak del Pezzo surfaces. As a result, we classify smooth projective surfaces admitting a full cyclic strong exceptional collection of line bundles. Also, we provide an example of a weak del Pezzo surface of degree 2 and a full strong exceptional collection of line bundles on it which does not come from augmentations, thus answering a question by Hille and Perling.
