  We present an intriguing and precise interplay between algebraic geometry and
the phenomenology of generations of particles. Using the electroweak sector of
the MSSM as a testing ground, we compute the moduli space of vacua as an
algebraic variety for multiple generations of Standard Model matter and Higgs
doublets. The space is shown to have Calabi-Yau, Grassmannian, and toric
signatures which sensitively depend on the number of generations of leptons, as
well as inclusion of Majorana mass terms for right-handed neutrinos. We
speculate as to why three generations is special.
