-- -*- M2-comint -*- {* hash: 247620444 *}

i1 : R = QQ[a,b,c,d]/(a^4+b^4+c^4+d^4);

i2 : X = Proj R

o2 = X

o2 : ProjectiveVariety

i3 : Omega = cotangentSheaf X

o3 = cokernel {2} | c  0  0  d  0   a3  b3 0  |
              {2} | a  d  0  0  b3  -c3 0  0  |
              {2} | -b 0  d  0  a3  0   c3 0  |
              {2} | 0  b  a  0  -d3 0   0  c3 |
              {2} | 0  -c 0  a  0   -d3 0  b3 |
              {2} | 0  0  -c -b 0   0   d3 a3 |

                                         6
o3 : coherent sheaf on X, quotient of OO  (-2)
                                        X

i4 : HH^1(Omega)

       20
o4 = QQ

o4 : QQ-module, free

i5 : F = sheaf coker matrix {{a,b}}

o5 = cokernel | a b |

                                         1
o5 : coherent sheaf on X, quotient of OO
                                        X

i6 : module F

o6 = cokernel | a b |

                            1
o6 : R-module, quotient of R

i7 :