On the Birational Geometry of Sextic Threefold Hypersurfaces in P (1, 1, 2, 2, 3)

Key Points

• The aim is to explore the birational properties of sextic hypersurfaces in the weighted projective space.
• Analyzed the structure of sextic hypersurfaces within the context of birational geometry.
• Focused on quasi-smooth variants of these hypersurfaces.
• Applied theoretical techniques in algebraic geometry to derive conclusions.
• Proved that any quasi-smooth hypersurface of degree 6 in the specified space is not rational.