Towards \(A+B\) theory in conifold transitions for Calabi-Yau threefolds. (English) Zbl 1423.14242
Summary: For projective conifold transitions between Calabi-Yau threefolds \(X\) and \(Y\), with \(X\) close to \(Y\) in the moduli, we show that the combined information provided by the \(A\) model (Gromov-Witten theory in all genera) and \(B\) model (variation of Hodge structures) on \(X\), linked along the vanishing cycles, determines the corresponding combined information on \(Y\). Similar result holds in the reverse direction when linked with the exceptional curves.
MSC:
14J33 | Mirror symmetry (algebro-geometric aspects) |
14J32 | Calabi-Yau manifolds (algebro-geometric aspects) |
14N35 | Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects) |
53D45 | Gromov-Witten invariants, quantum cohomology, Frobenius manifolds |