Gromov-Witten theory via Kuranishi structures

Mohammad Farajzadeh Tehrani; Kenji Fukaya

Gromov-Witten theory via Kuranishi structures

Symplectic Geometry 2017-01-27 v1 Algebraic Geometry

Authors: Mohammad Farajzadeh Tehrani , Kenji Fukaya

Abstract

In this expository manuscript, we review the construction of Gromov-Witten virtual fundamental class via FOOO's theory of Kuranishi structures for moduli spaces of pseudo-holomorphic maps defined on closed Riemann surfaces. We consider constraints coming from the ambient space and Deligne-Mumford moduli, called primary insertions, as well as intrinsic classes such as $\psi$ -classes and Hodge classes.

Keywords

Gromov-Witten theory Kuranishi structure virtual fundamental class pseudo-holomorphic map moduli space primary insertion Hodge class

Cite

@article{arxiv.1701.07821,
  title  = {Gromov-Witten theory via Kuranishi structures},
  author = {Mohammad Farajzadeh Tehrani and Kenji Fukaya},
  journal= {arXiv preprint arXiv:1701.07821},
  year   = {2017}
}

Comments

This article is based on the original article of Fukaya-Ono and subsequent articles of Fukaya-Oh-Ohta-Ono and covers the relevant parts of their theory of Kuranishi structures that is needed to define Gromov-Witten VFC. Proof of the gluing theorem and related estimates are not included

Gromov-Witten theory via Kuranishi structures

Abstract

Keywords

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