Degenerations of quintic threefolds and their lines (Q1821169)

Let \(V_ t: GH+tF\) be a 1-parameter degeneration of a quintic 3-fold \(V_ t\subset {\mathbb{P}}^ 4\) to a union of a quadric G and a cubic H, and let C be the curve \(F\cap G\cap H\). Under genericity assumptions, as \(t\to 0\) the 2875 lines of \(V_ t\) tend to 1300 lines of G meeting C\ 3- times and 1575 lines of H meeting C twice. The methods and the interest of the problem come from a paper by \textit{H. Clemens} [Publ. Math., Inst. Hautes Étud. Sci. 58, 231-250 (1983; Zbl 0529.14002)].