The modular group for the total ancestor potential of Fermat simple elliptic singularities

2014/01/13 by Milanov, Todor, Shen, Yefeng
#2010: Primary 14N35 #33C05 #Algebraic Geometry (math.AG) #FOS: Mathematics #Secondary 33C75

paper · doi:10.48550/arxiv.1401.2725

Abstract

In a series of papers \citeKS,MR, Krawitz, Milanov, Ruan, and Shen have verified the so-called Landau-Ginzburg/Calabi-Yau (LG/CY) correspondence for simple elliptic singularities E_N^(1,1) (N=6,7,8). As a byproduct it was also proved that the orbifold Gromov--Witten invariants of the orbifold projective lines ℙ¹_3,3,3, ℙ¹_4,4,2, and ℙ¹_6,3,2 are quasi-modular forms on an appropriate modular group. While the modular group for ℙ¹_3,3,3 is Γ(3), the modular groups in the other two cases were left unknown. The goal of this paper is to prove that the modular groups in the remaining two cases are respectively Γ(4) and Γ(6).

Related

• Gromov-Witten theory of elliptic orbifold P¹ and quasi-modular forms
• Landau-Ginzburg/Calabi-Yau Correspondence of all Genera for Elliptic Orbifold \mathbbp¹
• 6-dimensional FJRW theories of the simple-elliptic singularities
• Indefinite theta functions arising in Gromov-Witten Theory of elliptic orbifolds
• Gromov-Witten theory and cycle-valued modular forms