Beijing Institute of Mathematical Sciences and Applications

The Donaldson–Fujiki moment map picture interprets the scalar curvature of a Kahler metric as a moment map for the action of Hamiltonian diffeomorphisms on the space of compatible complex structures. We generalize this picture to other scalar curvature quantities using equivariant determinant line bundles. Interpreting the (nonexistent) complexified orbit as varying Kahler potentials while keeping the complex structure fixed, these moment maps arise as variations of the log of the Quillen metric on determinant line bundles. This also naturally yields other GIT counterparts, such as log-norm functionals and weights.