Landau-Ginzburg/Calabi-Yau Correspondence of all Genera for Elliptic Orbifold $p^1$

Abstract

In this paper, we establish the convergence for Gromov-Witten invariant of elliptic orbifold ${\mathbb{P}}^1$ with type $(3,3,3),(4,4,2)$ and $(6,3,2)$. We also prove the mirror theorems of Gromov-Witten theory for those orbifolds and FJRW theory of elliptic singularities. Using T.Milanov and Y. Ruan's work, we prove the Landau-Ginzburg/Calabi-Yau correspondence of all genera for the above three types of elliptic orbifold ${\mathbb{P}}^1$.

References in corpus (2)

• FJRW rings and Landau-Ginzburg Mirror Symmetry
• Gromov-Witten theory of elliptic orbifold P^1 and quasi-modular forms

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• A Landau-Ginzburg mirror theorem via matrix factorizations
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• From primitive form to mirror symmetry
• On Frobenius Manifolds from Gromov--Witten Theory of Orbifold Projective Lines with $r$ orbifold points
• Remarks on Symplectic Geometry