Mathematical Research Letters

Volume 28 (2021)

Number 4

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

Pages: 1217 – 1225

DOI:  https://dx.doi.org/10.4310/MRL.2021.v28.n4.a10

Author

Vlad Matei (Raymond and Beverly School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel)

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 $d \to \infty$. We also discuss some consequence of this result for the moduli space of smooth degree $d$ hypersurfaces in $\mathbb{P}^n$.

This material is based upon work supported by the National Science Foundation under Grant Number DMS 1641020.

Received 24 October 2019

Accepted 2 June 2020

Published 22 November 2021