Corpus ID: 216553618

# On the liftability of the automorphism group of smooth hypersurfaces of the projective space

```@article{GonzlezAguilera2020OnTL,
title={On the liftability of the automorphism group of smooth hypersurfaces of the projective space},
author={V{\'i}ctor Gonz{\'a}lez-Aguilera and Alvaro Liendo and Pedro Montero},
journal={arXiv: Algebraic Geometry},
year={2020}
}```
• Published 2020
• Mathematics
• arXiv: Algebraic Geometry
• Let \$X\$ be a smooth hypersurface of dimension \$n\geq 1\$ and degree \$d\geq 3\$ in the projective space given as the zero set of a homogeneous form \$F\$. If \$(n,d)\neq (1,3), (2,4)\$ it is well known that every automorphism of \$X\$ extends to an automorphism of the projective space, i.e., \$\operatorname{Aut}(X)\subseteq \operatorname{PGL}(n+2,\mathbb{C})\$. We say that the automorphism group \$\operatorname{Aut}(X)\$ is \$F\$-liftable if there exists a subgroup of \$\operatorname{GL}(n+2,\mathbb{C… CONTINUE READING

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