In a current project with Ritwik Mukherjee and Martijn Kool, we attempt to prove a variant of the Gottsche conjecture by looking at the number of δ-nodal degree d planar curves in P 3 intersecting the right number of generic lines. We wish to show that for d ≥ δ this number is given by a universal polynomial of some determined degree involving d. We attempt to do this by performing a relative version over the Grassmannian Gr(3, 4) ∼ = P 3∗ of the computations of Kool-Thomas-Shende in their proof of the Gottsche conjecture. We also wish to verify our answers by comparing to direct counts using different methods developed by Ritwik and Zinger and possibly also comparing our results to certain Gromov-Witten calculations by Pandharipande. Perhaps a more ambitious aim will be to also consider suitable generalisations to planar curves in higher dimensional projective spaces.