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arXiv · 2012.12046

Rationality problem of two-dimensional quasi-monomial group actions

Akinari Hoshi·Hidetaka Kitayama
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Abstract

The rationality problem of two-dimensional purely quasi-monomial actions was solved completely by Hoshi, Kang and Kitayama [HKK]. As a generalization, we solve the rationality problem of two-dimensional quasi-monomial actions under the condition that the actions are defined within the base field. In order to prove the theorem, we give a brief review of the Severi-Brauer variety with some examples and rationality results. We also use a rationality criterion for conic bundles of $\mathbb{P}^1$ over non-closed fields.

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Akinari Hoshi, Hidetaka Kitayama. 2020-12-22. Rationality problem of two-dimensional quasi-monomial group actions. https://arxiv.org/abs/2012.12046

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