Freezing of moduli by $N=2\mathrm{}$ dyons

In $N=2\mathrm{}$ ungauged supergravity we have found the most general double-extreme dyonic black holes with arbitrary number $n_v$ of constant vector multiplets and $n_h$ of constant hypermultiplets. They are double extreme: (1) supersymmetric with coinciding horizons; (2) the mass for a given set of quantized charges is extremal. The spacetime is of the Reissner-Nordström form and the vector multiplet moduli depend on dyon charges. As an example we display $n_v$ complex moduli as functions of $2(n_v+1)$ electric and magnetic charges in a model related to a classical Calabi-Yau moduli space. A specific case includes the complex $S$, $T$, $U$ moduli depending on four electric and four magnetic charges of 4 U(1) gauge groups.