Numerical bounds for degenerations of surfaces of general type

Abstract

This paper considers bounds on the numerical properties of degenerations of surfaces of general type. Under suitable assumptions, are give explicit bounds for the number of singularities outside the double curve and for the number of components in a relative canonical model. We also give bounds for the index of singularities in a special case, which illustrates clearly the reason behind the bounds for the index in a relatively minimal permissible degeneration.