Embedding Theorems for Calabi--Yau Conifolds
Algebraic Geometry
2025-10-17 v2 Complex Variables
Differential Geometry
Abstract
We prove that compact Calabi--Yau varieties with certain isolated singularities are projective. In dimension 3 we do this by analysis, supposing given conifold metrics. In higher dimensions it follows more readily from Ohsawa's degenerate spectral sequence.
Cite
@article{arxiv.2403.01200,
title = {Embedding Theorems for Calabi--Yau Conifolds},
author = {Yohsuke Imagi},
journal= {arXiv preprint arXiv:2403.01200},
year = {2025}
}
Comments
The results themselves are not new. Theorem 1.1 follows from the Beauville-Bogomolov decomposition [2] and Theorem 1.5 from Namikawa's theorem (IJM 2002, Theorem 6)