Uniqueness of birational structures on Inoue surfaces

ShengYuan Zhao

Uniqueness of birational structures on Inoue surfaces

Complex Variables 2021-01-21 v2 Algebraic Geometry Geometric Topology

Authors: ShengYuan Zhao

Abstract

We prove that the natural $(\operatorname{Aff} _2(\mathbf{C}),\mathbf{C}^2)$ -structure on an Inoue surface is the unique $(\operatorname{Bir}(\mathbb{P}^2),\mathbb{P}^2(\mathbf{C}))$ -structure, generalizing a result of Bruno Klingler which asserts that the natural $(\operatorname{Aff}_2(\mathbf{C}),\mathbf{C}^2)$ -structure is the unique $(\operatorname{PGL} _3(\mathbf{C}),\mathbb{P}^2(\mathbf{C}))$ -structure.

Cite

@article{arxiv.1909.13266,
  title  = {Uniqueness of birational structures on Inoue surfaces},
  author = {ShengYuan Zhao},
  journal= {arXiv preprint arXiv:1909.13266},
  year   = {2021}
}

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36 pages

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