Rationality of an \(S_6\)-Invariant Quartic 3-Fold

  • Ilya KarzhemanovEmail author


We complete the study of rationality problem for hypersurfaces \(X_t\subset \mathbb {P}^4\) of degree 4 invariant under the action of the symmetric group \(S_6\).


Quartic 3-fold Ordinary double point Rationality 

Mathematics Subject Classification

14E08 14E30 14M10 



Some parts of the paper were prepared during my visits to AG Laboratory at HSE (Moscow) and Miami University (US). I am grateful to these Institutions and people there for hospitality. Also thanks to anonymous referee for valuable comments. The work was supported by World Premier International Research Initiative (WPI), MEXT, Japan, by Grant-in-Aid for Scientific Research (26887009) from Japan Mathematical Society (Kakenhi), and by the Russian Academic Excellence Project 5-100.


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© Sociedade Brasileira de Matemática 2019

Authors and Affiliations

  1. 1.Moscow Institute of Physics and TechnologyInstitutskij pereulokDolgoprudnyiRussia

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