• Corpus ID: 221090291

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

  title={On Emergent Geometry of the Gromov-Witten Theory of Quintic Calabi-Yau Threefold},
  author={Jian Zhou},
  journal={arXiv: Mathematical Physics},
  • Jian Zhou
  • Published 8 August 2020
  • Mathematics
  • arXiv: Mathematical Physics
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 K\"ahler structure. 
Geometry and arithmetic of integrable hierarchies of KdV type. I. Integrality
For each of the simple Lie algebras g = Al, Dl or E6, we show that the all-genera one-point FJRW invariants of g-type, after multiplication by suitable products of Pochhammer symbols, are the


Gromov - Witten invariants and integrable hierarchies of topological type
We outline two approaches to the construction of integrable hierarchies associated with the theory of Gromov - Witten invariants of smooth projective varieties. We argue that a comparison of these
Quantum Cohomology at Higher Genus: Topological Recursion Relations and Virasoro Conditions
We construct topological recursion relations (TRR’s) at higher genera g ≥ 2 for general 2-dimensional topological field theories coupled to gravity. These TRR’s when combined with Virasoro conditions
Topological Recursions of Eynard–Orantin Type for Intersection Numbers on Moduli Spaces of Curves
We prove that the Virasoro constraints satisfied by the higher Weil–Petersson volumes of moduli spaces of curves are equivalent to Eynard–Orantin topological recursions for some spectral curve. This
We present a universal construction of almost duality for Frobenius man- ifolds. The analytic setup of this construction is described in details for the case of semisimple Frobenius manifolds. We
On Itzykson-Zuber Ansatz
Abstract We apply the renormalized coupling constants and Virasoro constraints to derive the Itzykson-Zuber Ansatz on the form of the free energy in 2D topological gravity. We also treat the 1D
Counting higher genus curves in a Calabi-Yau manifold
Topological recursion relations in genus 2
In Part 1 of this paper, we study gravitational descendents of Gromov-Witten invariants for general projective manifolds, applying the Behrend-Fantechi construction of the virtual fundamental
Hodge integrals and Gromov-Witten theory
Integrals of the Chern classes of the Hodge bundle in Gromov-Witten theory are studied. We find a universal system of differential equations which determines the generating function of these
Normal forms of hierarchies of integrable PDEs, Frobenius manifolds and Gromov - Witten invariants
We present a project of classification of a certain class of bihamiltonian 1+1 PDEs depending on a small parameter. Our aim is to embed the theory of Gromov - Witten invariants of all genera into the