## Journal of Differential Geometry

### 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.

#### Article information

Source
J. Differential Geom., Volume 110, Number 3 (2018), 495-541.

Dates
First available in Project Euclid: 17 November 2018

https://projecteuclid.org/euclid.jdg/1542423628

Digital Object Identifier
doi:10.4310/jdg/1542423628

Mathematical Reviews number (MathSciNet)
MR3880232

Zentralblatt MATH identifier
06982218

#### Citation

Lee, Yuan-Pin; Lin, Hui-Wen; Wang, Chin-Lung. Towards $A+B$ theory in conifold transitions for Calabi–Yau threefolds. J. Differential Geom. 110 (2018), no. 3, 495--541. doi:10.4310/jdg/1542423628. https://projecteuclid.org/euclid.jdg/1542423628