Abstract

Let $X$ be a Calabi-Yau $3$-fold equipped with a real structure and a compatible Lefschetz $K3$ fibration. Assuming that the real locus of $X$ is nonempty and contains no critical points of the fibration, we show that each connected component admits a nowhere-vanishing harmonic $1$-form with respect to the metric induced by the collapsing Ricci-flat Kähler metrics on $X$. We then apply this to the Joyce-Karigiannis construction to produce compact $7$-manifolds with full $G_2$ holonomy, and also to construct families of pairwise disjoint special Lagrangian submanifolds. This is joint work with Daniel Platt and Calum Spicer.

Organizers

Nicolau Sarquis Aiex (NTNU), Siao-Hao Guo (NTU), Chao-Ming Lin (NTU), Wei-Bo Su (NCU), Chung-Jun Tsai (NTU)