Projective embedding of degenerating family of Kähler-Einstein manifolds with normal crossing limit

Abstract

We study the Bergman embeddings of degenerating families of Kähler-Einstein manifolds of negative curvature. We show that when the central fiber has only simple normal crossing singularities, we can construct orthonormal bases so that the induced Bergman embeddings converge to the Bergman embedding of the limit space together with multi-bubbles.