-- -*- M2-comint -*- hash: 16990418382345161113

i1 : PP3 = toricProjectiveSpace 3;

i2 : assert(isSmooth PP3 and isProjective PP3)

i3 : K = toricDivisor PP3

o3 = - PP3  - PP3  - PP3  - PP3
          0      1      2      3

o3 : ToricDivisor on PP3

i4 : assert(all(entries K, i -> i === -1) and isWellDefined K)

i5 : omega = OO K

          1
o5 = OO    (-4)
       PP3

o5 : coherent sheaf on PP3, free of rank 1

i6 : assert(HH^3(PP3, OO_PP3(-7) ** omega) === HH^0(PP3, OO_PP3(7)))

i7 : X = normalToricVariety({{1,0,0},{0,1,0},{0,0,1},{0,-1,-1},{-1,0,-1},{-2,-1,0}},{{0,1,2},{0,1,3},{1,3,4},{1,2,4},{2,4,5},{0,2,5},{0,3,5},{3,4,5}});

i8 : assert(isComplete X and not isProjective X and not isSmooth X)

i9 : KX = toricDivisor X

o9 = - X  - X  - X  - X  - X  - X
        0    1    2    3    4    5

o9 : ToricDivisor on X

i10 : assert(all(entries KX, i -> i === -1) and isWellDefined KX)

i11 : isCartier KX

o11 = false

i12 : omegaX = OO KX

         1
o12 = OO   (-3, -3, -4)
        X

o12 : coherent sheaf on X, free of rank 1

i13 : assert( HH^0(X, OO_X(1,2,5)) === HH^3(X, OO_X(-1,-2,-5) ** omegaX) )

i14 : 
