An Analytic Proof of the Stable Reduction Theorem

Abstract

The stable reduction theorem says that a family of curves of genus $g\ge 2$ over a punctured curve can be uniquely completed (after possible base change) by inserting certain stable curves at the punctures. We give a new proof of this result for curves defined over $\mathbb{C}$ using the Kähler-Einstein metrics on the fibers to obtain the limiting stable curves at the punctures.

References in corpus (2)

• Degeneration of Kahler-Einstein manifolds of negative scalar curvature
• Riemannian geometry of Kahler-Einstein currents III: compactness of Kahler-Einstein manifolds of negative scalar curvature