We generalize the results of Marinescu-Savale to families of Bochner Laplacians. This particularly leads to the fiberwise expansion for families Bergman kernels of horizontally semi-positive index bundles. Our results include the case of highest weight families. The proofs are based on Ma-Zhang's description for the curvature of the index bundle as a fiberwise Toeplitz operator as well as on methods from sub-Riemannian geometry. Based on joint work with X. Ma and G. Marinescu.
Bochner Laplacians and Bergman kernels for families
02.06.2025 11:30 - 13:00
Organiser:
Luke Edholm
Location:
BZ09