Iranian Mathematical SocietyJournal of the Iranian Mathematical Society2717-16121120200301Canonical sections of Hodge bundles on moduli spaces9711510418610.30504/jims.2020.104186ENK.LiuDepartment of Mathematics, University of California at Los Angeles, Los Angeles, CA 90095-1555, USAY.ShenDepartment of Mathematics, Nanjing University, Nanjing 210093, P.R.ChinaJournal Article20200206We review recent works in [K. Liu, S. Rao, and X. Yang, Quasi-isometry and deformations of Calabi Yau manifolds, Inventiones mathematicae, 199(2) (2015), 423–453] and [K. Liu and Y. Shen, Moduli spaces as ball quotients I, local theory, preprint] on geometry of sections of Hodge bundles and their applications to moduli spaces.http://jims.ims.ir/article_104186_5aeacde0efd83615df987f55d36727c2.pdf