SUSY N = 2 hyperelliptic curve from N = 1 effective potential

We derive the singularity conditions of the N = 1 generalized (general Yukawa couplings and quark masses) form of hyperelliptic curves of SU(Nc) with Nf flavors. The results reproduce the known form of N = 2 curves when the Yukawa couplings and the quark masses reduce to those of N = 2. We obtained these curves by determining the dependence of the unbroken SU(2) gaugino condensation on the couplings in the moduli source terms which break N = 2 SQCD to N = 1SU(Nc) gauge theory with the quarks and the adjoint matter, Φ. The degenerate component of the diagonalized classical vacuum expectation value of Φ is shown to be explicitly written in terms of these couplings, which enables us to determine the form of the gaugino condensation.