Landau-Ginzburg/Calabi-Yau Correspondence of all Genera for Elliptic Orbifold \mathbbp¹

2011/06/30 by Krawitz, Marc, Shen, Yefeng
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1106.6270

Abstract

In this paper, we establish the convergence for Gromov-Witten invariant of elliptic orbifold ℙ¹ 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 ℙ¹.

Related

• Gromov-Witten theory of elliptic orbifold P¹ and quasi-modular forms
• Gromov--Witten invariants for mirror orbifolds of simple elliptic singularities
• Equivariant Gromov-Witten Theory of GKM Orbifolds
• Gromov-Witten theory of toroidal orbifolds and GIT wall-crossing
• On the Elliptic Genus and Mirror Symmetry