Abstract
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.
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