This investigation reveals the non-rationality of sextic hypersurfaces in weighted projective space, indicating significant geometric features.
We investigate birational properties of hypersurfaces of degree $$6$$ in the weighted projective space P(1,1,2,2,3) . In particular, we prove that any such quasi-smooth hypersurface is not rational.
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Yuri Prokhorov (2025) studied this question.
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