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SpecialFanoFourfolds :: parametrize(SpecialGushelMukaiFourfold)

parametrize(SpecialGushelMukaiFourfold) -- rational parametrization

Synopsis

Description

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 0.147833 seconds

o2 : MultirationalMap (birational map from PP^4 to X)
i3 : time describe phi
     -- used 0.9553 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

See also

Ways to use this method: