Givental-Type Reconstruction at a Nonsemisimple Point

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Autoren

  • Alexey Basalaev
  • Nathan Priddis

Organisationseinheiten

Externe Organisationen

  • Universität Mannheim
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Details

OriginalspracheEnglisch
Seiten (von - bis)333-369
Seitenumfang37
FachzeitschriftMichigan Mathematical Journal
Jahrgang67
Ausgabenummer2
PublikationsstatusVeröffentlicht - Mai 2018

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.

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Givental-Type Reconstruction at a Nonsemisimple Point. / Basalaev, Alexey; Priddis, Nathan.
in: Michigan Mathematical Journal, Jahrgang 67, Nr. 2, 05.2018, S. 333-369.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Basalaev A, Priddis N. Givental-Type Reconstruction at a Nonsemisimple Point. Michigan Mathematical Journal. 2018 Mai;67(2):333-369. doi: 10.48550/arXiv.1605.07862, 10.1307/mmj/1523584849
Basalaev, Alexey ; Priddis, Nathan. / Givental-Type Reconstruction at a Nonsemisimple Point. in: Michigan Mathematical Journal. 2018 ; Jahrgang 67, Nr. 2. S. 333-369.
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title = "Givental-Type Reconstruction at a Nonsemisimple Point",
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{\textquoteright}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{\textquoteright}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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TY - JOUR

T1 - Givental-Type Reconstruction at a Nonsemisimple Point

AU - Basalaev, Alexey

AU - Priddis, Nathan

N1 - Funding information: AB was partially supported by the DGF grant He2287/4–1 (SISYPH).

PY - 2018/5

Y1 - 2018/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85047181248&partnerID=8YFLogxK

UR - https://arxiv.org/abs/1605.07862

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