论文标题
在4度上的四倍数二次富集计数4 del Pezzo表面
A quadratically enriched count of lines on a degree 4 del Pezzo surface
论文作者
论文摘要
在代数封闭的磁场上，在4度DEL Pezzo表面上有16行，但是对于其他字段，情况更加微妙。为了改善在完美领域的枚举结果，Kass和Wickelgren引入了一种类似于使用PoinCare-Hopf定理对平滑矢量束的零部分进行计数的方法。但是，Kass-Wickelgren的技术需要枚举问题，以满足某种类型的可提供性条件。在4 del pezzo表面上计数线的问题无法满足这种定向性条件，因此本文的大多数工作都致力于解决此问题。我们通过限制在满足方向性条件的开放式集合中来做到这一点，并检查获得的计数是否明确定义，类似于Larson和Vogt开发的方法。
Over an algebraically closed field k, there are 16 lines on a degree 4 del Pezzo surface, but for other fields the situation is more subtle. In order to improve enumerative results over perfect fields, Kass and Wickelgren introduce a method analogous to counting zeroes of sections of smooth vector bundles using the Poincare-Hopf theorem. However, the technique of Kass-Wickelgren requires the enumerative problem to satisfy a certain type of orientability condition. The problem of counting lines on a degree 4 del Pezzo surface does not satisfy this orientability condition, so most of the work of this paper is devoted to circumventing this problem. We do this by restricting to an open set where the orientability condition is satisfied, and checking that the count obtained is well-defined, similarly to an approach developed by Larson and Vogt.
