Summary: Bounding singular surfaces of general type
Valery Alexeev 1 and Shigefumi Mori 2
1 Department of Mathematics, University of Georgia, Athens GA 30605, USA
2 Research Institute for Mathematical Sciences
Kyoto University, Kyoto 6068502, JAPAN
Abstract. We provide simpler proofs of several boundedness theorems, contained
in in articles , , for log surfaces of general type with semi log canonical sin
gularities. At the same time, we make these proofs effective, with explicit upper
In this work, we present several effective boundedness results for various in
variants of singular surfaces. The most important application of these results
is the existence of the moduli space of semilog canonical surfaces of gen
eral type. The construction of this moduli space was started in , and the
boundedness provides the final necessary step to complete it.
This paper was written in 1995 for a planned volume on moduli of surfaces
of general type, which has not yet been published. Therefore, with the editors'
consent, we are publishing the paper independently.
Time, meanwhile, was not standing still, and there have been new develop
ments in the field, none of which supersede the results of our work. The most