The twistor discriminant locus of the Fermat cubic

摘要

We consider the discriminant locus of the Fermat cubic under the twistor fibration CP3 ⟶ S4. We show that it has a conformal symmetry group of order 72. Using these symmetries we reduce the problem of computing the topology of this discriminant locus to a computationally feasible problem which we solve using the cylindrical algebraic decomposition algorithm.