Quadratic types and the dynamic Euler number of lines on a quintic threefold

We provide a geometric interpretation of the local contribution line to count lines on quintic threefold over field k characteristic not equal 2, that is, we define type and show it coincides with index at corresponding zero section Sym5S⁎→Gr(2,5) defined by threefold. Furthermore, dynamic Euler number which allows us compute A1-Euler as sum contributions zeros non-isolated deform general deformation. As an example quadratic 2875 distinguished Fermat computes Sym5S⁎→Gr(2,5). Combining those two results get when is 2 or 5∑Trk(l)/k(Type(l))=1445〈1〉+1430〈−1〉∈GW(k) where runs