next | previous | forward | backward | up | index | toc

# toGrass(EmbeddedProjectiveVariety) -- embedding of an ordinary Gushel-Mukai fourfold or a del Pezzo variety into GG(1,4)

## Synopsis

• Function: toGrass
• Usage:
toGrass X
• Inputs:
• X, , an ordinary Gushel-Mukai fourfold, or a del Pezzo variety of dimension at least 4 (e.g., a sixfold projectively equivalent to $\mathbb{G}(1,4)\subset\mathbb{P}^9$)
• Outputs:
• , an embedding of $X$ into the Grassmannian $\mathbb{G}(1,4)\subset\mathbb{P}^9$, Plücker embedded

## Description

 i1 : x = gens ring PP_(ZZ/33331)^8; i2 : X = projectiveVariety ideal(x_4*x_6-x_3*x_7+x_1*x_8, x_4*x_5-x_2*x_7+x_0*x_8, x_3*x_5-x_2*x_6+x_0*x_8+x_1*x_8-x_5*x_8, x_1*x_5-x_0*x_6+x_0*x_7+x_1*x_7-x_5*x_7, x_1*x_2-x_0*x_3+x_0*x_4+x_1*x_4-x_2*x_7+x_0*x_8); o2 : ProjectiveVariety, 5-dimensional subvariety of PP^8 i3 : time toGrass X warning: clearing value of symbol x to allow access to subscripted variables based on it : debug with expression debug 9868 or with command line option --debug 9868 -- used 9.999s (cpu); 5.33148s (thread); 0s (gc) o3 = multi-rational map consisting of one single rational map source variety: 5-dimensional subvariety of PP^8 cut out by 5 hypersurfaces of degree 2 target variety: GG(1,4) ⊂ PP^9 o3 : MultirationalMap (rational map from X to GG(1,4)) i4 : show oo o4 = -- multi-rational map -- ZZ source: subvariety of Proj(-----[x , x , x , x , x , x , x , x , x ]) defined by 33331 0 1 2 3 4 5 6 7 8 { x x - x x + x x , 4 6 3 7 1 8 x x - x x + x x , 4 5 2 7 0 8 x x - x x + x x + x x - x x , 3 5 2 6 0 8 1 8 5 8 x x - x x + x x + x x - x x , 1 5 0 6 0 7 1 7 5 7 x x - x x + x x + x x - x x + x x 1 2 0 3 0 4 1 4 2 7 0 8 } ZZ target: subvariety of Proj(-----[x , x , x , x , x , x , x , x , x , x ]) defined by 33331 0,1 0,2 1,2 0,3 1,3 2,3 0,4 1,4 2,4 3,4 { x x - x x + x x , 2,3 1,4 1,3 2,4 1,2 3,4 x x - x x + x x , 2,3 0,4 0,3 2,4 0,2 3,4 x x - x x + x x , 1,3 0,4 0,3 1,4 0,1 3,4 x x - x x + x x , 1,2 0,4 0,2 1,4 0,1 2,4 x x - x x + x x 1,2 0,3 0,2 1,3 0,1 2,3 } -- rational map 1/1 -- map 1/1, one of its representatives: { 5418x - 821x + 5588x - 3585x - 1758x - 15576x + 9147x - 14993x - 4736x , 0 1 2 3 4 5 6 7 8 11632x - 4732x - 10523x - 11526x - 1991x - 1831x - 9701x + 12320x - 2015x , 0 1 2 3 4 5 6 7 8 16371x - 7244x + 4935x + 15111x + 3749x - 12977x + 15511x + 7287x + 6751x , 0 1 2 3 4 5 6 7 8 - 13960x - 3219x + 8239x - 10597x + 7747x + 273x - 6285x + 2934x - 4471x , 0 1 2 3 4 5 6 7 8 - 12638x - 12017x - 2651x + 7012x - 9505x + 3559x - 2170x - 59x - 265x , 0 1 2 3 4 5 6 7 8 - 4096x + 10456x - 2284x + 11208x + 5756x - 6263x + 599x + 7817x - 6486x , 0 1 2 3 4 5 6 7 8 5896x + 11711x - 9239x + 9726x + 9682x + 2295x - 6875x - 16024x - 7246x , 0 1 2 3 4 5 6 7 8 - 8687x + 14564x + 3651x - 6141x - 7924x + 3227x - 5479x + 13427x + 11982x , 0 1 2 3 4 5 6 7 8 89x + 11710x + 1284x - 12079x + 11673x - 2256x + 12732x - 7459x - 5231x , 0 1 2 3 4 5 6 7 8 - 25x + 12923x + 1000x + 871x + 15902x - 3782x - 7479x - 5250x + 11717x 0 1 2 3 4 5 6 7 8 }