Gromov-Witten invariants of Fano threefolds of genera 6 and 8

Abstract

The 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 corrected

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Cited by in corpus (5)

• Mirror symmetry for Pfaffian Calabi-Yau 3-folds via conifold transitions
• Deresonating a Tate period
• A comparison of Landau-Ginzburg models for odd dimensional Quadrics
• Quantum cohomology of smooth complete intersections in weighted projective spaces and singular toric varieties
• Rational curves on prime Fano threefolds of index 1