Inequalities for semi-stable surface fibrations, and their relation to the Coleman-Oort conjecture
arXiv:1405.4531
Abstract
I give a simplified proof of one of the main results in the recent preprint arXiv:1311.5858 by X. Luo and K. Zuo. Furthermore, I discuss the relation with the Coleman-Oort conjecture on special curves in the Torelli locus.
Main changes for this version: an addiononal discussion on how Arakelov-type inequalities (as discussed in the previous version) relate to the Coleman-Oort conjecture, and changed the title accordingly. Accepted by "Pure and Applied Mathematics Quarterly"