Uniqueness modulo reduction of Bergman meromorphic compactifications of canonically embeddable Bergman manifolds (Q2928497)

A Bergman manifold is a complex manifold \(X\) such that the Bergman kernel form induces a Kähler metric on the manifold \(X\). The Bergman manifold \(X\) is canonically embeddable if the canonical map \(\Phi_X : X \rightarrow \mathbb P^\infty\) defined by any Hilbert basis of square-integrable holomorphic \(n\)-forms is a holomorphic embedding. The author defines a Bergman meromorphic compactification as a compactification \(X \subset Z\) by a compact complex manifold satisfying certain extension properties with respect to the Bergman kernel form on \(X\). He proves that if a canonically embeddable Bergman manifold has a Bergman meromorphic compactification, then there is a minimal element among all compactifications of this type and this minimal element is essentially unique. He also proves that the compact complex manifold \(Z\) is always Moishezon and studies some examples in detail.NEWLINENEWLINEFor the entire collection see [Zbl 1291.00056].