Gromov-Witten Theory of Quotients of Fermat
                    Calabi-Yau varieties

Iritani, Hiroshi; Milanov, Todor; Ruan, Yongbin; Shen, Yongjun

doi:10.1090/memo/1310

Cited by 6 publications

(2 citation statements)

References 58 publications

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“…and certain quotients thereof. The invariants and corresponding genus zero mirror symmetry for the CY variety M have been extensively explored [CdLOGP91, Giv96, Giv98, LLY97, LLY98], our main focus is then the orbifold GW invariants of the quotients of M, see e.g., [LS14,IMRS21] for related studies.…”

Section: A-modelmentioning

confidence: 99%

Twisted Sectors in Calabi-Yau Type Fermat Polynomial Singularities and Automorphic Forms

Zhang¹,

Zhou²

2021

Preprint

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We study one-parameter deformations of Calabi-Yau type Fermat polynomial singularities along degree-one directions. We show that twisted sectors in the vanishing cohomology are components of automorphic forms for certain triangular groups. We prove consequently that genus zero Gromov-Witten generating series of the corresponding Fermat Calabi-Yau varieties are components of automorphic forms. The main tools we use are mixed Hodge structures for quasihomogeneous polynomial singularities, Riemann-Hilbert correspondence, and genus zero mirror symmetry.

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Section: A-modelmentioning

confidence: 99%

Twisted Sectors in Calabi-Yau Type Fermat Polynomial Singularities and Automorphic Forms

Zhang¹,

Zhou²

2021

Preprint

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“…The equivalence of 2d quantum field theories is a longstanding interesting topic in mathematical physics, including the following two examples: (1)the equivalence between Gromov-Witten theories under K-equivariant birational transformation [LR01, LLW10, Rua06, BG09, CIJ18, EW12]; (2)the Landau-Ginzburg/Calabi-Yau correspondence (equivalence between Gromov-Witten theory of CY hypersurface and Fan-Jarivs-Ruan-Witten theory of a Landau-Ginzburg model) [CR10,CIR14,IMRS21].…”

Section: Introductionmentioning

confidence: 99%

Seiberg Duality conjecture for star-shaped quivers and finiteness of Gromov-Witten thoery for D-type quivers

Zhang¹

2023

Preprint

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This is the second work on Seiberg Duality. This work proves that the Seiberg duality conjecture holds for star-shaped quivers: the Gromov-Witten theories for two mutation-related varieties are equivalent.In particular, it is known that a D-type quiver goes back to itself after finite times quiver mutations, and we further prove that Gromov-Witten theory together with kähler variables of a D 3 -type quiver variety return to the original ones after finite times quiver mutations.

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Higher Genus FJRW Theory for Fermat Cubic Singularity

Wang

2021

Acta. Math. Sin.-English Ser.

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Gromov-Witten Theory of Quotients of Fermat Calabi-Yau varieties

Cited by 6 publications

References 58 publications

Twisted Sectors in Calabi-Yau Type Fermat Polynomial Singularities and Automorphic Forms

Twisted Sectors in Calabi-Yau Type Fermat Polynomial Singularities and Automorphic Forms

Seiberg Duality conjecture for star-shaped quivers and finiteness of Gromov-Witten thoery for D-type quivers

Higher Genus FJRW Theory for Fermat Cubic Singularity

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