f = beauvilleMap X
Smooth intersections of three quadrics in $\mathbb{P}^7$ are birational to quadric surface bundles over $\mathbb{P}^2$ with discriminant curve of degree 8. This is a construction of Beauville; see e.g. Proposition 6 in the paper Intersections of three quadrics in P7, by B. Hassett, A. Pirutka, and Y. Tschinkel.





The object beauvilleMap is a method function.