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We extend Igusa's map $\rho$ to modular forms which vanish on thehyperelliptic locus of the Siegel upper half-plane. The lowest non-vanishingderivatives of such modular forms are computed with the help of the generalThomae formula, they serve as vector-valued modular forms. This approach isillustrated by examples in genera $3$ and $4$.

Igusa's map on modular forms vanishing on the hyperelliptic locus