On the birational geometry of sextic threefold hypersurface in $\mathbf{P}(1,1,2,2,3)$

TL;DR

This paper studies degree 6 hypersurfaces in a specific weighted projective space and proves that all such quasi-smooth hypersurfaces are not rational, contributing to understanding their birational geometry.

Contribution

It establishes the non-rationality of all quasi-smooth sextic hypersurfaces in the weighted projective space $ extbf{P}(1,1,2,2,3)$, a new result in birational geometry.

Findings

All quasi-smooth sextic hypersurfaces are non-rational.

Provides birational classification insights for hypersurfaces in weighted projective spaces.

Advances understanding of the birational properties of degree 6 hypersurfaces.

Abstract

We investigate birational properties of hypersurfaces of degree $6$ in the weighted projective space $\mathbf{P}(1,1,2,2,3)$. In particular, we prove that any such quasi-smooth hypersurface is not rational.