  A long-standing question in string theory is to find the explicit expression
of the bosonic measure, a crucial issue also in determining the superstring
measure. Such a measure was known up to genus three. Belavin and Knizhnik
conjectured an expression for genus four which has been proved in the framework
of the recently introduced vector-valued Teichmueller modular forms. It turns
out that for g>3 the bosonic measure is expressed in terms of such forms. In
particular, the genus four Belavin-Knizhnik "wonderful formula" has a
remarkable extension to arbitrary genus whose structure is deeply related to
the characterization of the Jacobian locus. Furthermore, it turns out that the
bosonic string measure has an elegant geometrical interpretation as generating
the quadrics in P^{g-1} characterizing the Riemann surface. All this leads to
identify forms on the Siegel upper half-space that, if certain conditions
related to the characterization of the Jacobian are satisfied, express the
bosonic measure as a multiresidue in the Siegel upper half-space. We also
suggest that it may exist a super analog on the super Siegel half-space.
