Deformations of Zappatic stable surfaces and their Galois covers

Abstract

This paper considers some algebraic surfaces that can deform to planar Zappatic stable surfaces with a unique singularity of type En. We prove that the Galois covers of these surfaces are all simply connected of general type, for n >= 4, and we give a formula for Chern numbers of such Galois covers. As an application, we prove that such surfaces do not exist for n>30. Furthermore, Kollar improves the result to n>9 in Appendix 5.