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math.DG2006
Bergman kernels and symplectic reduction
Xiaonan Ma, Weiping Zhang
We generalize several recent results concerning the asymptotic expansions of Bergman kernels to the framework of geometric quantization and establish an asymptotic symplectic ident…
math.DG2006
Superconnection and family Bergman kernels
Xiaonan Ma, Weiping Zhang
We establish an asymptotic expansion for families of Bergman kernels. The key idea is to use the superconnection as in the local family index theorem.
math.DG2006
η-invariant and flat vector bundles II
Xiaonan Ma, Weiping Zhang
We first apply the method and results in the previous paper to give a new proof of a result (hold in ) of Gilkey on the variation of h-invariants associated to no…