2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/134965The aim of this paper is to prove Golyshev's conjecture in the cases of Fano threefolds $V_{10}$ and $V_{14}$. This conjecture states modularity of D3 equations for smooth Fano threefolds with Picard group Z. More precisely, we find counting matrices of prime two-pointed Gromov-Witten invariants for them. For this we use the method that lets us find Gromov-Witten invariants of complete intersections in varieties whose invariants are (partially) known.12 pages, 1 figure, typos correctedAlgebraic GeometryMathematical Physics14N35; 14J45text