Deformations of Zappatic stable surfaces and their Galois covers
Algebraic Geometry
2024-04-08 v3
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.
Cite
@article{arxiv.2402.06017,
title = {Deformations of Zappatic stable surfaces and their Galois covers},
author = {Meirav Amram and Cheng Gong and JiaLi Mo},
journal= {arXiv preprint arXiv:2402.06017},
year = {2024}
}
Comments
The paper includes an appendix written by Janos Kollar