TL;DR
This paper surveys the geometries associated with supersymmetric fivebranes in M-theory, focusing on 4-plane geometries in eight dimensions, and explores their self-duality properties.
Contribution
It provides new results and detailed computations on 4-plane geometries in eight dimensions related to supersymmetric fivebranes.
Findings
New results on 4-plane geometries in eight dimensions
Analysis of generalized self-dualities in these geometries
Detailed computational methods for calibrated geometries
Abstract
We present a survey of the calibrated geometries arising in the study of the local singularity structure of supersymmetric fivebranes in M-theory. We pay particular attention to the geometries of 4-planes in eight dimensions, for which we present some new results as well as many details of the computations. We also analyse the possible generalised self-dualities which these geometries can afford.
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