论文标题
二次类型和动态的欧拉数五重的线路数
Quadratic types and the dynamic Euler number of lines on a quintic threefold
论文作者
论文摘要
我们提供了一条线对线上的局部贡献的几何解释，该线在不等于2的字段上的三倍k上的线计数，也就是说，我们定义了Quintic三倍的线的类型，并表明它与Sym^5 s^5 s^* - > gr（2、5）的sym^5 s^5 s^5 s^5 s^5 s^5 s^5 s^5 s^5 s^5 s^5 s^* s^* - > gr（2、5）定义的局部索引重合。此外，我们定义了动态欧拉数，这使我们能够计算A^1-euler编号作为具有非分离零的部分的零零贡献的总和，该零件的零件零件的局部贡献与一般变形变形。作为一个例子，我们提供了二次计数，为2875个区分线上的二号线三倍，该线计算sym^5 s^* - > gr的动态欧拉数（2，5）。结合了这两个结果，我们得到一般五重的三倍上的线类型的总和为1445 <1> + 1430 <-1>当k是一个特征的特征领域，不等于2或5时。
We provide a geometric interpretation of the local contribution of a line to the count of lines on a quintic threefold over a field k of characteristic not equal to 2, that is, we define the type of a line on a quintic threefold and show that it coincides with the local index at the corresponding zero of the section of Sym^5 S^* -> Gr(2, 5) defined by the threefold. Furthermore, we define the dynamic Euler number which allows us to compute the A^1-Euler number as the sum of local contributions of zeros of a section with non-isolated zeros which deform with a general deformation. As an example we provide a quadratic count of 2875 distinguished lines on the Fermat quintic threefold which computes the dynamic Euler number of Sym^5 S^* -> Gr(2, 5). Combining those two results we get that the sum of the types of lines on a general quintic threefold is 1445<1> + 1430<-1> in GW(k) when k is a field of characteristic not equal to 2 or 5.
