All genus open mirror symmetry for footballs
We prove an all genus full descendant open mirror symmetry for footballs. The B-model is given by the Chekhov-Eynard-Orantin topological recursion on the mirror curve.
math.AG↗
arXiv subjects
Jinghao Yu
Publications and source records attributed to Jinghao Yu.
On one-leg orbifold topological vertex in refined Gromov-Witten theory
We define the one-leg orbifold topological vertex in refined Gromov-Witten theory \cite{BS24}. There are two cases where the leg is effective or gerby. The main result of this paper is the computation of the effective case. In the smooth case, this result matches the one-leg refined vertex in \cite{IKV09}. As an application, we compute the refined Gromov-Witten invariants of the local football.
math.AG↗
Mirror symmetry and open/closed correspondence for the projective line
We study the open/closed correspondence for the projective line via mirror symmetry. More explicitly, we establish a correspondence between the generating function of disk Gromov-Witten invariants of the complex projective line $\mathbb{P}^1$ with boundary condition specified by an $S^1$-invariant Lagrangian sub-manifold $L$ and the asymptotic expansion of the $I$-function of a toric surface $\mathcal{S}$.
math.AG↗
All genus open mirror symmetry for the projective line
We prove that the Chekhov-Eynard-Orantin recursion on the mirror curve of $\mathbb{P}^1$ encodes all genus equivariant open Gromov-Witten invariants of $(\mathbb{P}^1, \mathbb{R}\mathbb{P}^1)$. This result can be viewed as an all genus equivariant open mirror symmetry for $(\mathbb{P}^1, \mathbb{R}\mathbb{P}^1)$.
math.AG↗
Torus knots in Lens spaces, open Gromov-Witten invariants, and topological recursion
Starting from a torus knot $\mathcal{K}$ in the lens space $L(p,-1)$, we construct a Lagrangian sub-manifold $L_{\mathcal{K}}$ in $\mathcal{X}=\big(\mathcal{O}_{\mathbb{P}^1}(-1)\oplus \mathcal{O}_{\mathbb{P}^1}(-1)\big)/\mathbb{Z}_p$ under the conifold transition. We prove a mirror theorem which relates the all genus open-closed Gromov-Witten invariants of $(\mathcal{X},L_{\mathcal{K}})$ to the topological recursion on the B-model spectral curve. This verifies a conjecture in \cite{Bor-Bri} in the case of lens space.
math.AG↗