Towards $A+B$ theory in conifold transitions for Calabi-Yau threefolds

Abstract

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.

47 pages, references updated. To appear in J. Diff. Geometry

References in corpus (1)

• Invariance of Quantum Rings under Ordinary Flops II: A quantum Leray--Hirsch theorem

Cited by in corpus (2)

• Cubic Extremal Transition and Gromov-Witten Theory
• Tautological systems under the conifold transition on $G(2,4)$