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Asymptotic expansion of the variation of the Quillen metric and its moment map interpretation

组织者

林耿龙 , Enric Sole Farre , 张蓥莹

演讲者

Kiyoon Eum

时间

2025年12月02日 20:00 至 21:30

地点

Online

线上

Zoom 928 682 9093 (BIMSA)

摘要

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.