Projective embedding of stably degenerating sequence of hyperbolic Riemann surfaces

Abstract

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

12 pages

References in corpus (1)

• Boundary asymptotics of the relative Bergman kernel metric for curves