2023/02/17 by Daniela Paiva, Ana Quedo, Paiva, Daniela +1
Mathematics · #Algebraic Geometry and Number Theory #Advanced Differential Equations and Dynamical Systems #History and Theory of Mathematics
paper · pdf · doi:10.48550/arxiv.2302.09014
In this paper, we consider the problem of determining which automorphisms of a smooth quartic surface S ⊂ ℙ3 are induced by a Cremona transformation of ℙ3. We provide the first steps towards a complete solution of this problem when ρ(S)=2. In particular, we give several examples of quartics whose automorphism groups are generated by involutions, but no non-trivial automorphism is induced by a Cremona transformation of ℙ3, giving a negative answer for Oguiso's question of whether every automorphism of finite order of a smooth quartic surface S⊂ ℙ3 is induced by a Cremona transformation.