  In this paper we study automorphic correction of the hyperbolic Kac-Moody
algebra $E_{10}$, using the Borcherds product for O(10,2) attached to a weakly
holomorphic modular form of weight -4 for $SL_2(\mathbb Z)$. We also clarify
some aspects of automorphic correction for Lorentzian Kac-Moody algebras and
give heuristic reasons for the expectation that every Lorentzian Kac-Moody
algebra has an automorphic correction.
