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

2015/02/11 by Yuan‐Pin Lee, Lee, Yuan-Pin, Hui-Wen Lin +3 · 1 citation
Mathematics · #14D05 #14D07 #14J32 #14N32 #81T45 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1502.03277

openalex publication_date 2015/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

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

Cited by

• Cubic Extremal Transition and Gromov-Witten Theory

Related

• Mirror symmetry for Pfaffian Calabi-Yau 3-folds via conifold transitions
• Calabi-Yau threefolds across quadratic singularities
• Gromov--Witten/Pandharipande--Thomas correspondence via conifold transitions
• An introduction to conifold transitions
• Geometric Transitions and Mixed Hodge Structures