On the Brauer group of a generic Godeaux surface

Theodosis Alexandrou

On the Brauer group of a generic Godeaux surface

Algebraic Geometry 2022-07-19 v1

Authors: Theodosis Alexandrou

Abstract

Let $X$ be a Godeaux surface over $\mathbb{C}$ and $q_{X}\colon Y\to X$ be its universal cover. We show that the pullback map $q^{*}_{X}\colon Br(X)\to Br(Y)$ is injective if $\rho(Y)=9$ . Our arguments rely on a degeneration technique that also applies to other examples.

Keywords

godeaux surface brauer group universal cover pullback map degeneration technique

Cite

@article{arxiv.2207.08042,
  title  = {On the Brauer group of a generic Godeaux surface},
  author = {Theodosis Alexandrou},
  journal= {arXiv preprint arXiv:2207.08042},
  year   = {2022}
}

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21 pages

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