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

Extending the Belavin-Knizhnik "wonderful formula" by the characterization of the Jacobian