This function is mainly based on results contained in the classical paper Algebraic varieties with canonical curve sections, by L. Roth. In some examples, more strategies are available. For instance, if $X\subset\mathbb{P}^7$ is a 4-dimensional linear section of $\mathbb{G}(1,4)\subset\mathbb{P}^9$, then by passing Strategy=>1 (which is the default choice) we get the inverse of the projection from the plane spanned by a conic contained in $X$; while with Strategy=>2 we get the projection from the unique $\sigma_{2,2}$-plane contained in $X$ (Todd's result).
i1 : G'1'4 = projectiveVariety Grass(1,4,ZZ/65521 ); X = G'1'4 * random({{1},{1}},0_G'1'4); o1 : ProjectiveVariety, GG(1,4) o2 : ProjectiveVariety, 4-dimensional subvariety of PP^9 |
i3 : ? X o3 = 4-dimensional subvariety of PP^9 cut out by 7 hypersurfaces of degrees 1^2 2^5 |
i4 : time parametrizeFanoFourfold X -- used 1.24855 seconds o4 = multi-rational map consisting of one single rational map source variety: PP^4 target variety: 4-dimensional subvariety of PP^9 cut out by 7 hypersurfaces of degrees 1^2 2^5 dominance: true degree: 1 o4 : MultirationalMap (birational map from PP^4 to X) |
The object parametrizeFanoFourfold is a method function with options.