Embedding Theorems for Calabi--Yau Conifolds

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.

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)