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Any Cremona transformation of \(\mathbb {P}^3\) stabilizing a smooth quartic surface \(S\subset \mathbb {P}^3\) induces an automorphism on S. The converse problem of determining which automorphisms of S are restrictions of Cremona transformations of the ambient space \(\mathbb {P}^3\) is still open. In this survey paper, we provide the answer of this problem for quartic surfaces with Picard rank two.

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Cremona Transformations of \(\mathbb {P}^3\) Stabilizing Quartic Surfaces

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  • 发表日期：

    2026年

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  • Daniela Paiva

摘要

Any Cremona transformation of \(\mathbb {P}^3\) stabilizing a smooth quartic surface \(S\subset \mathbb {P}^3\) induces an automorphism on S. The converse problem of determining which automorphisms of S are restrictions of Cremona transformations of the ambient space \(\mathbb {P}^3\) is still open. In this survey paper, we provide the answer of this problem for quartic surfaces with Picard rank two.