Holomorphic curves in moduli spaces of polarized Abelian varieties

Abstract

We first prove a version of tautological inequality (proposed by McQuillan) for an open Riemann surface by using stochastic calculus. Then we use it to establish a Second Main Theorem of Nevanlinna theory for a smooth logarithmic pair (X, D). As a consequence, we also set up a Second Main Theorem of holomorphic curves into some moduli spaces of polarized Abelian varieties intersecting boundary divisors.Recently, Sun [10] considered the conjecture and proved an inequality