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May 2018 Givental-Type Reconstruction at a Nonsemisimple Point
Alexey Basalaev, Nathan Priddis
Michigan Math. J. 67(2): 333-369 (May 2018). DOI: 10.1307/mmj/1523584849


We consider the orbifold curve that is a quotient of an elliptic curve 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 E/Z4 and FJRW theory of the pair defined by the polynomial x4+y4+z2 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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Alexey Basalaev. Nathan Priddis. "Givental-Type Reconstruction at a Nonsemisimple Point." Michigan Math. J. 67 (2) 333 - 369, May 2018.


Received: 19 September 2016; Revised: 5 September 2017; Published: May 2018
First available in Project Euclid: 13 April 2018

zbMATH: 06914766
MathSciNet: MR3802257
Digital Object Identifier: 10.1307/mmj/1523584849

Primary: 14J33, 14N35
Secondary: 14B05

Rights: Copyright © 2018 The University of Michigan


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Vol.67 • No. 2 • May 2018
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