Generalising G2 geometry: involutivity, moment maps and moduli

Singular Moment Maps and Quaternionic Geometry

Special Metrics in G2 Geometry

We discuss metrics with holonomy G2 by presenting a few crucial examples and review a series of G2 manifolds constructed via solvable Lie groups, obtained in [15]. These carry two related distinguished metrics, one negative Einstein and the other in the conformal class of a Ricci-flat metric, plus other features considered definitely worth investigating.

Classification and Moduli Kähler Potentials of G2 Manifolds

Compact manifolds ofG2 holonomy may be constructed by dividing a seven-torus by some discrete symmetry group and then blowing up the singularities of the resulting orbifold. We classify possible group elements that may be used in this construction and use this classification to find a set of possible orbifold groups. We then derive the moduli Kähler potential for M-theory on the resulting class...

Dirac Geometry, Quasi–Poisson Actions and D/G–Valued Moment Maps

We study Dirac structures associated with Manin pairs (d, g) and give a Dirac geometric approach to Hamiltonian spaces with D/G-valued moment maps, originally introduced by Alekseev and Kosmann-Schwarzbach [3] in terms of quasi-Poisson structures. We explain how these two distinct frameworks are related to each other, proving that they lead to isomorphic categories of Hamiltonian spaces. We str...

Moduli of Spherical Varieties and Log Geometry

We give moduli interpretations using log geometry of the main components of the moduli spaces of polarized spherical varieties defined by Alexeev and Brion. The key new insight is that logarithmic structures alone do not suffice to give a good moduli interpretation. Instead we introduce a notion of an enriched log structure which is a logarithmic structure together with some extra data related ...