# CoherentSheaf / CoherentSheaf -- quotient of coherent sheaves

## Synopsis

• Operator: /
• Usage:
F / G
• Inputs:
• Outputs:
• , the quotient sheaf F/G

## Description

We compute the cohomology of two sheaves supported on an elliptic curve.
 i1 : X = Proj(QQ[x,y,z]) o1 = X o1 : ProjectiveVariety i2 : I = ideal(y^2*z-x*(x-z)*(x-11*z)) 3 2 2 2 o2 = ideal(- x + 12x z + y z - 11x*z ) o2 : Ideal of QQ[x..z] i3 : N = (sheaf module I)/(sheaf module I^2) o3 = subquotient (| -x3+12x2z+y2z-11xz2 |, | x6-24x5z-2x3y2z+166x4z2+24x2y2z2+y4z2-264x3z3-22xy2z3+121x2z4 |) 1 o3 : coherent sheaf on X, subquotient of OO X i4 : G = OO_X^1/I o4 = cokernel | -x3+12x2z+y2z-11xz2 | 1 o4 : coherent sheaf on X, quotient of OO X i5 : HH^1(G) 1 o5 = QQ o5 : QQ-module, free i6 : HH^1(N) 9 o6 = QQ o6 : QQ-module, free