Average size of the automorphism group of smooth projective hypersurfaces over finite fields

Vlad Matei

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arXiv · 1910.09145

Average size of the automorphism group of smooth projective hypersurfaces over finite fields

Vlad Matei

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Abstract

In this paper, we show that the average size of the automorphism group over $\mathbb{F}_q$ of a smooth degree $d$ hypersurface in $\mathbb{P}^{n}_{\mathbb{F}_q}$ is equal to $1$ as $d\rightarrow \infty$. We also discuss some consequence of this result for the moduli space of smooth degree $d$ hypersurfaces in $\mathbb{P}^n$.

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Vlad Matei. 2019-10-21. Average size of the automorphism group of smooth projective hypersurfaces over finite fields. https://arxiv.org/abs/1910.09145

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