Off-diagonal estimates of partial Bergman kernels on $S^1$-symmetric Kähler manifolds (Ood Shabtai -Universités de Lille & Paris Cité)

We establish local asymptotic estimates of partial Bergman kernels on closed
$S^1$-symmetric K\"{a}hler manifolds. The main result addresses   the scaling asymptotics of partial Bergman kernels
at generic off-diagonal points in which they are not negligible. The example of the two-dimensional sphere
will be discussed in detail.