Given a compact quantizable pseudo-Kähler manifold (M,ω) of constant signature, there exists a Hermitian line bundle (L, h) over M with curvature -2πiω. We shall show that the asymptotic expansion of the Bergman kernels for L⊗k-valued (0, q)-forms implies more or less immediately a number of analogues of well-known results, such as Kodaira embedding theorem and Tian’s almost-isometry theorem.
Galasso, A., Hsiao, C. (2024). Embedding theorems for quantizable pseudo-Kähler manifolds. BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA [10.1007/s40574-024-00445-4].
Embedding theorems for quantizable pseudo-Kähler manifolds
Galasso, A.
;
2024
Abstract
Given a compact quantizable pseudo-Kähler manifold (M,ω) of constant signature, there exists a Hermitian line bundle (L, h) over M with curvature -2πiω. We shall show that the asymptotic expansion of the Bergman kernels for L⊗k-valued (0, q)-forms implies more or less immediately a number of analogues of well-known results, such as Kodaira embedding theorem and Tian’s almost-isometry theorem.
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