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arXiv · 2303.01408

The field of moduli of sets of points in $\mathbb{P}^{2}$

Giulio Bresciani
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Abstract

For every $n\ge 6$, we give an example of a finite subset of $\mathbb{P}^{2}$ of degree $n$ which does not descend to any Brauer-Severi surface over the field of moduli. Conversely, for every $n\le 5$ we prove that a finite subset of degree $n$ always descends to a $0$-cycle on $\mathbb{P}^{2}$ over the field of moduli.

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Giulio Bresciani. 2023-03-02. The field of moduli of sets of points in $\mathbb{P}^{2}$. https://arxiv.org/abs/2303.01408

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