On birational boundedness of some Calabi-Yau hypersurfaces
Taro Sano
TL;DR
This paper proves the birational boundedness of certain Calabi-Yau hypersurfaces and explores the boundedness properties of specific K3 surfaces, contributing to the understanding of their classification and moduli.
Contribution
It establishes birational boundedness for anti-canonical hypersurfaces forming 3-fold plt pairs and analyzes the boundedness of a collection of Du Val K3 surfaces.
Findings
Anti-canonical hypersurfaces forming 3-fold plt pairs are birationally bounded.
A collection of Du Val K3 surfaces is birationally bounded but not bounded.
The results advance the classification theory of Calabi-Yau and K3 surfaces.
Abstract
We show the birational boundedness of anti-canonical irreducible hypersurfaces which form 3-fold plt pairs. We also treat a collection of Du Val K3 surfaces which is birationally bounded but unbounded.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Geometric Analysis and Curvature Flows