  We geometrically describe a canonical sequence of modular blowups of the
relative Picard stack of the Artin stack of pre-stable genus two curves. The
final blowup stack locally diagonalizes certain tautological derived objects.
This implies a resolution of the primary component of the moduli space of genus
two stable maps to projective space and meanwhile makes the whole moduli space
admit only normal crossing singularities. Our approach should extend to higher
genera.
