i1 : PP3 = projectiveSpace 3; |
i2 : OmegaPP3 = cotangentSheaf PP3 o2 = cokernel {2} | x_2 0 0 x_3 | {2} | x_0 x_3 0 0 | {2} | -x_1 0 x_3 0 | {2} | 0 x_1 x_0 0 | {2} | 0 -x_2 0 x_0 | {2} | 0 0 -x_2 -x_1 | 6 o2 : coherent sheaf on PP3, quotient of OO (-2) PP3 |
i3 : prune exteriorPower(3,OmegaPP3) 1 o3 = OO (-4) PP3 o3 : coherent sheaf on PP3 |
i4 : prune exteriorPower(3,OmegaPP3) === OO toricDivisor PP3 o4 = true |
i5 : X = hirzebruchSurface 2; |
i6 : OmegaX = cotangentSheaf X o6 = cokernel {2, 0} | 2x_1x_3 | {-1, 2} | x_0 | {-1, 2} | -x_2 | 1 2 o6 : coherent sheaf on X, quotient of OO (-2,0) ++ OO (1,-2) X X |
i7 : prune exteriorPower(dim X, OmegaX) 1 o7 = OO (0,-2) X o7 : coherent sheaf on X |
i8 : prune exteriorPower(dim X, OmegaX) === OO toricDivisor X o8 = true |
i9 : Rho = {{1,0,0},{0,1,0},{0,0,1},{0,-1,-1},{-1,0,-1},{-2,-1,0}}; |
i10 : Sigma = {{0,1,2},{0,1,3},{1,3,4},{1,2,4},{2,4,5},{0,2,5},{0,3,5},{3,4,5}}; |
i11 : Y = normalToricVariety(Rho,Sigma); |
i12 : isSmooth Y o12 = false |
i13 : isProjective Y o13 = false |
i14 : OmegaY = cotangentSheaf Y o14 = cokernel {2, 0, 2} | x_2x_4 0 2x_0x_4 0 0 0 x_0x_2 0 0 | {2, 2, 0} | x_1x_5 x_0x_5 0 0 0 0 0 x_0x_1 0 | {0, 2, 3} | 0 x_2x_3 -x_1x_3 0 x_1x_2 0 0 0 0 | {2, 2, 2} | -x_3 0 0 x_0 0 0 0 0 0 | {2, 2, 3} | 0 -x_4 0 0 0 x_1 0 0 0 | {2, 2, 3} | 0 0 -x_5 0 0 0 0 0 x_2 | {2, 2, 4} | 0 0 0 -x_4 -2x_4 -2x_3 -x_3 0 0 | {2, 3, 3} | 0 0 0 -x_5 x_5 0 0 -x_3 -x_3 | {3, 2, 3} | 0 0 0 0 0 -x_5 x_5 -x_4 2x_4 | 1 1 1 1 2 1 1 1 o14 : coherent sheaf on Y, quotient of OO (-2,0,-2) ++ OO (-2,-2,0) ++ OO (0,-2,-3) ++ OO (-2,-2,-2) ++ OO (-2,-2,-3) ++ OO (-2,-2,-4) ++ OO (-2,-3,-3) ++ OO (-3,-2,-3) Y Y Y Y Y Y Y Y |
i15 : prune exteriorPower(dim Y, OmegaY) 1 o15 = OO (-3,-3,-4) Y o15 : coherent sheaf on Y |
i16 : prune exteriorPower(dim Y, OmegaY) === OO toricDivisor Y o16 = true |