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We consider the orbifold curve that is a quotient of an elliptic curve $\mathcal{E}$ by a cyclic group of order 4. We develop a systematic way to obtain a Givental-type reconstruction of Gromov–Witten theory of the orbifold curve via the product of the Gromov–Witten theories of a point. This is done by employing mirror symmetry and certain results in FJRW theory. In particular, we present the particular Givental’s action giving the CY/LG correspondence between the Gromov–Witten theory of the orbifold curve $\mathcal{E}/\mathbb{Z}_{4}$ and FJRW theory of the pair defined by the polynomial $x^{4}+y^{4}+z^{2}$ and the maximal group of diagonal symmetries. The methods we have developed can easily be applied to other finite quotients of an elliptic curve. Using Givental’s action, we also recover this FJRW theory via the product of the Gromov–Witten theories of a point. Combined with the CY/LG action, we get a result in “pure” Gromov–Witten theory with the help of modern mirror symmetry conjectures.

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Project Euclid (Hosted at Cornell University Library)  

Autor(es)

Basalaev, Alexey -  Priddis, Nathan - 

Id.: 71305350

Idioma: inglés  - 

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Palabras clave14J33 - 

Tipo de recurso: Text  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

: Copyright 2018 The University of Michigan

Formatos:  application/pdf - 

Requerimientos técnicos:  Browser: Any - 

Relación: [References] 0026-2285
[References] 1945-2365

Fecha de contribución: 13-may-2018

Contacto:

Localización:
* Michigan Math. J. 67, iss. 2 (2018), 333-369
* doi:10.1307/mmj/1523584849

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