Givental-type reconstruction at a nonsemisimple point

Alexey Basalaev, Nathan Priddis

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)333-369
Number of pages37
JournalMichigan Mathematical Journal
Volume67
Issue number2
DOIs
Publication statusPublished - May 2018

Fingerprint

Dive into the research topics of 'Givental-type reconstruction at a nonsemisimple point'. Together they form a unique fingerprint.

Cite this