# 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} }

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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