On geometry of Fano threefold hypersurfaces
Hamid Ahmadinezhad, Ivan Cheltsov, Jihun Park
TL;DR
This paper establishes a precise criterion for the birational rigidity of quasi-smooth Fano threefold hypersurfaces, linking it directly to their Fano index, and thereby advances understanding of their geometric classification.
Contribution
It provides a complete characterization of birational rigidity for quasi-smooth Fano threefold hypersurfaces based on their Fano index, a significant step in algebraic geometry.
Findings
Quasi-smooth Fano threefold hypersurfaces are birationally rigid if and only if they have Fano index one.
The paper clarifies the relationship between Fano index and birational properties of threefold hypersurfaces.
It offers a criterion to determine birational rigidity in this class of algebraic varieties.
Abstract
We prove that a quasi-smooth Fano threefold hypersurface is birationally rigid if and only if it has Fano index one.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric and Algebraic Topology · Algebraic Geometry and Number Theory