Energy bounds and vanishing results for the Gromov–Witten invariants of the projective space

Aleksey Zinger

doi:10.1016/j.geomphys.2019.103479

Energy bounds and vanishing results for the Gromov–Witten invariants of the projective space

Aleksey Zinger

Mathematics

Stony Brook University

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

Abstract

We describe generating functions for arbitrary-genus Gromov–Witten invariants of the projective space with any number of marked points explicitly. The structural portion of this description gives rise to uniform energy bounds and vanishing results for these invariants. They suggest deep conjectures relating Gromov–Witten invariants of symplectic manifolds to the energy of pseudo-holomorphic maps and the expected dimension of their moduli space.

Original language	English
Article number	103479
Journal	Journal of Geometry and Physics
Volume	145
DOIs	https://doi.org/10.1016/j.geomphys.2019.103479
State	Published - Nov 2019

Keywords

Gromov–Witten invariants
Upper bounds

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10.1016/j.geomphys.2019.103479

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title = "Energy bounds and vanishing results for the Gromov–Witten invariants of the projective space",

abstract = "We describe generating functions for arbitrary-genus Gromov–Witten invariants of the projective space with any number of marked points explicitly. The structural portion of this description gives rise to uniform energy bounds and vanishing results for these invariants. They suggest deep conjectures relating Gromov–Witten invariants of symplectic manifolds to the energy of pseudo-holomorphic maps and the expected dimension of their moduli space.",

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AB - We describe generating functions for arbitrary-genus Gromov–Witten invariants of the projective space with any number of marked points explicitly. The structural portion of this description gives rise to uniform energy bounds and vanishing results for these invariants. They suggest deep conjectures relating Gromov–Witten invariants of symplectic manifolds to the energy of pseudo-holomorphic maps and the expected dimension of their moduli space.

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KW - Upper bounds

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DO - 10.1016/j.geomphys.2019.103479

M3 - Article

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VL - 145

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

M1 - 103479

ER -

Energy bounds and vanishing results for the Gromov–Witten invariants of the projective space

Abstract

Keywords

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