  We study the gluing theory of Riemann surfaces using formal algebraic
geometry, and give computable relations between the associated parameters for
different gluing processes. As its application to the Liouville conformal field
theory, we construct the sheaf of tempered conformal blocks on the moduli space
of pointed Riemann surfaces which satisfies the factorization property and has
a natural action of the Teichm\"{u}ller groupoid.
