Order of an automorphism of a quasi-smooth hypersurface in weighted projective spaces
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| Ana Palomino |
| Universidad de Talca |
| Abstract |
| Let \(X=V(F)\) be a hypersurface of \(\mathbb{P}_a^{n+1}\) given as the zero set of a homogeneous form \(F\in \mathbb{C}[x_0 ,\cdots , x_{n+1}]\) of degree \(d\). The group of linear automorphisms, denoted by \({\rm Lin}(X)\), is the subgroup of \({\rm Aut}(X)\) of automorphisms that extends to an automorphism of the ambient space \(\mathbb{P}_a^{n+1}\), i.e., \[{\rm Lin}(X)=\{\varphi\in {\rm Aut}(\mathbb{P}_a^{n+1})|\ \varphi(X)=X\}.\] |
| Recently [Ess24], shows that under certain conditions, we have that group \({\rm Lin}(X)={\rm Aut}(X)\), and furthermore, \({\rm Aut}(X)\) is finite. In this talk, we will apply this result to compute all the possible primes numbers that appear as the order of an automorphism of a well-formed quasi-smooth hyperspace in a weighted projective space. This is a generalization of [GAL13]. |
| References |
| [Ess24] Louis Esser. Automorphisms of weighted projective hypersurfaces, 2024. |
| [GAL13] Víctor González-Aguilera and Alvaro Liendo. On the order of an automorphism of a smooth hypersurface. Israel J. Math., 197(1):29–49, 2013. |
