The degeneration of Calabi-Yau 3-folds via 3-forms and the SYZ conjecture

Abstract

In this paper, we investigate the geometries associated with 3-forms of various orbital types on a symplectic 6-manifold. We demonstrate that certain unstable 3-forms, which naturally emerge from specific degenerations of Calabi-Yau structures, exhibit remarkably rich geometric properties. This, in turn, offers a novel perspective on the SYZ conjecture.

31 pages, comments are welcome! This paper partially supersedes arxiv: 2405.04827