Modular forms for the even unimodular lattice of signature (2,10)

Abstract

Some years ago, Borcherds described in [Bo1] two methods for constructing modular forms on modular varieties related to the orthogonal group ${\O}(2,n)$. They are the so called Borcherds' additive and multiplicative lifting. The multiplicative lifting has been used by Borcherds himself and other authors to construct modular forms with known vanishing locus and interesting properties. The additive lifting has been used to construct explicit maps from some modular varieties $\O(2,n)$. In this paper we try a more systematic treatment in certain level 2 cases giving connections with Kondo's works