Gluing theory for slc surfaces and threefolds in positive characteristic

Abstract

We develop a gluing theory in the sense of Kollár for slc surfaces and threefolds in positive characteristic. For surfaces we are able to deal with every positive characteristic p, while for threefolds we assume that p > 5. Along the way we study nodes in characteristic 2 and establish a theory of sources and springs à la Kollár for threefolds. We also give applications to the topology of lc centers on slc threefolds, and to the projectivity of the moduli space of stable surfaces in characteristic p > 5.