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Given a sequence of genus $g\geq 2$ curves converging to a punctured Riemannsurface with complete metric of constant Gaussian curvature $-1$.  we prove that the Kodaira embedding using orthonormal basis of the Bergmanspace of sections of a pluri-canonical bundle also converges to the embeddingof the limit space together with extra complex projective lines.

Projective embedding of stably degenerating sequence of hyperbolic Riemann surfaces