The goal of this paper and of a subsequent continuation is to find some
viable ansatze for the three-loop superstring chiral measure. For this, two
alternative formulas are derived for the two-loop superstring chiral measure.
Unlike the original formula, both alternates admit modular covariant
generalizations to higher genus. One of these two generalizations is analyzed
in detail in the present paper, with the analysis of the other left to the next
paper of the series.Comment: 30 page
