$G_2$-Grassmannians and derived equivalences

TL;DR

This paper establishes derived equivalences between specific non-compact Calabi-Yau 7-folds constructed as total spaces of rank 2 bundles over $G_2$-Grassmannians, extending previous results in lower dimensions.

Contribution

It proves the derived equivalence of two non-compact Calabi-Yau 7-folds related to $G_2$-Grassmannians, generalizing earlier work on Calabi-Yau 3-folds.

Findings

Derived equivalence of non-compact Calabi-Yau 7-folds.

Extension of Kuznetsov's methods to higher dimensions.

New insights into the geometry of $G_2$-Grassmannians.

Abstract

We prove the derived equivalence of a pair of non-compact Calabi-Yau 7-folds, which are the total spaces of certain rank 2 bundles on $G_2$-Grassmannians. The proof follows that of the derived equivalence of Calabi-Yau 3-folds in $G_2$-Grassmannians by Kuznetsov closely.