Bulk-Deformed Potentials for Toric Fano Surfaces, Wall-Crossing, and Period

Hansol Hong; Yu Shen Lin; Jingyu Zhao

doi:10.1093/imrn/rnaa357

Bulk-Deformed Potentials for Toric Fano Surfaces, Wall-Crossing, and Period

Hansol Hong, Yu Shen Lin, Jingyu Zhao

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We provide an inductive algorithm to compute the bulk-deformed potentials for toric Fano surfaces via wall-crossing techniques and a tropical-holomorphic correspondence theorem for holomorphic discs. As an application of the correspondence theorem, we also prove a big quantum period theorem for toric Fano surfaces, which relates the log descendant Gromov-Witten invariants with the oscillatory integrals of the bulk-deformed potentials.

Original language	English
Pages (from-to)	12699-12766
Number of pages	68
Journal	International Mathematics Research Notices
Volume	2022
Issue number	16
DOIs	https://doi.org/10.1093/imrn/rnaa357
Publication status	Published - 2022 Aug 1

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© 2021 The Author(s). Published by Oxford University Press. All rights reserved.

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1093/imrn/rnaa357

Cite this

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abstract = "We provide an inductive algorithm to compute the bulk-deformed potentials for toric Fano surfaces via wall-crossing techniques and a tropical-holomorphic correspondence theorem for holomorphic discs. As an application of the correspondence theorem, we also prove a big quantum period theorem for toric Fano surfaces, which relates the log descendant Gromov-Witten invariants with the oscillatory integrals of the bulk-deformed potentials.",

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AB - We provide an inductive algorithm to compute the bulk-deformed potentials for toric Fano surfaces via wall-crossing techniques and a tropical-holomorphic correspondence theorem for holomorphic discs. As an application of the correspondence theorem, we also prove a big quantum period theorem for toric Fano surfaces, which relates the log descendant Gromov-Witten invariants with the oscillatory integrals of the bulk-deformed potentials.

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Bulk-Deformed Potentials for Toric Fano Surfaces, Wall-Crossing, and Period

Abstract

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