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arXiv · 2209.10269

Embedding theorems for quantizable pseudo-Kähler manifolds

Andrea Galasso·Chin-Yu Hsiao
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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 $-2πi\,ω$. We shall show that the asymptotic expansion of the Bergman kernels for $L^{\otimes k}$-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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Andrea Galasso, Chin-Yu Hsiao. 2022-09-21. Embedding theorems for quantizable pseudo-Kähler manifolds. https://arxiv.org/abs/2209.10269

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