Smooth weighted hypersurfaces that are not stably rational
Takuzo Okada
TL;DR
This paper demonstrates that many smooth weighted hypersurfaces, including general Fano hypersurfaces of index one, are not stably rational, revealing new insights into their algebraic structure.
Contribution
It establishes the non-stable rationality of a broad class of smooth weighted hypersurfaces, including very general Fano hypersurfaces of index one.
Findings
Many smooth well formed weighted hypersurfaces are not stably rational
Very general smooth well formed Fano weighted hypersurfaces of index one are not stably rational
The results apply to hypersurfaces of dimension at least 3
Abstract
We prove the failure of stable rationality for many smooth well formed weighted hypersurfaces of dimension at least 3. It is in particular proved that a very general smooth well formed Fano weighted hypersurface of index one is not stably rational.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Geometric and Algebraic Topology