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arXiv · 2308.07904

Automorphisms of quartic del Pezzo surfaces in characteristic zero

Jonathan M. Smith
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Abstract

For each field $k$ of characteristic zero, we classify which groups act by automorphisms on a quartic del Pezzo surface over $k$. We also determine which groups act on $k$-rational, stably $k$-rational, or $k$-unirational quartic del Pezzo surfaces. For each group $G$ that is realized over $k$, we exhibit explicit equations for a quartic del Pezzo surface $X$ in $\mathbb{P}^4_k$ such that $G$ acts by automorphisms on $X$.

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Jonathan M. Smith. 2023-08-15. Automorphisms of quartic del Pezzo surfaces in characteristic zero. https://arxiv.org/abs/2308.07904

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