The 3-cuspidal quartic and braid monodromy of degree 4 coverings (original) (raw)

Motivated by the study of the differential and symplectic topology of (Z/2) 2-Galois covers of P 1 × P 1 , we determine the local braid monodromy of natural deformations of smooth (Z/2) 2-Galois covers of surfaces at the points where the branch curve has a nodal singularity. The study of the local deformed branch curves is solved via some interesting geometry of projectively unique objects: plane quartics with 3 cusps, which are the plane sections of the quartic surface having the twisted cubic as a cuspidal curve.