Universal degeneration of Riemann surfaces and fibered complex surfaces

Abstract

Based on Teichmüller theory, we construct a degenerating family of Riemann surfaces ${\bar{Y}}_g^{\mathrm{orb}}\to {\bar{M}}_g^{\mathrm{orb}}$ over the Deligne–Mumford compactification of the moduli space with the natural orbifold structure such that any fibered complex surface admitting unstable fibers can be pulled back from this family.