On Emergent Geometry of the Gromov-Witten Theory of Quintic Calabi-Yau Threefold

2020/08/08 by Jian Zhou, Zhou, Jian
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2008.03407

openalex publication_date 2020/08/08 · openalex created_date 2020/08/13 · openalex updated_date 2026/07/28

Abstract

We carry out the explicit computations that are used to write down the integrable hierarchy associated with the quintic Calabi-Yau threefold. We also do the calculations for the geometric structures emerging in the Gromov-Witten theory of the quintic, such as the Frobenius manifold structure and the special Kähler structure.

Citations

• Topological recursion relations in genus 2
• Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants
• Quantum Deformation Theory of the Airy Curve and Mirror Symmetry of a Point
• On Topological 1D Gravity. I

Related

• An effective theory of GW and FJRW invariants of quintics Calabi-Yau manifolds
• Gromov-Witten/Pairs correspondence for the quintic 3-fold
• Structure of Higher Genus Gromov-Witten Invariants of Quintic 3-folds
• Open Gromov-Witten theory on Calabi-Yau three-folds II
• A topological view of Gromov-Witten theory