Some special GM fourfolds are known to be rational. In this case, the function tries to obtain a birational map from $\mathbb{P}^4$ (or, e.g., from a quadric hypersurface in $\mathbb{P}^5$) to the fourfold.
i1 : X = specialGushelMukaiFourfold "tau-quadric"; o1 : ProjectiveVariety, GM fourfold containing a surface of degree 2 and sectional genus 0 |
i2 : time phi = parametrize X; -- used 0.295899 seconds o2 : MultirationalMap (birational map from PP^4 to X) |
i3 : time describe phi -- used 2.26236 seconds o3 = multi-rational map consisting of one single rational map source variety: PP^4 target variety: 4-dimensional subvariety of PP^8 cut out by 6 hypersurfaces of degree 2 base locus: surface in PP^4 cut out by 5 hypersurfaces of degrees 3^1 4^4 dominance: true multidegree: {1, 4, 8, 10, 10} degree: 1 degree sequence (map 1/1): [4] coefficient ring: ZZ/65521 |