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CoherentSheaf ^ ZZ -- direct sum

Synopsis

Operator: ^
Usage:

F^n
Inputs:
- F, a coherent sheaf, , or a a sheaf of rings
- n, an integer
Outputs:
- a coherent sheaf, the direct sum of n copies of F

Description

i1 : R = QQ[a..d]/(a*d-b*c)

o1 = R

o1 : QuotientRing

i2 : Q = Proj R

o2 = Q

o2 : ProjectiveVariety

i3 : OO_Q^5

        5
o3 = OO
       Q

o3 : coherent sheaf on Q, free of rank 5

i4 : IL = sheaf module ideal(a,b)

o4 = image | a b |

                                         1
o4 : coherent sheaf on Q, subsheaf of OO
                                        Q

i5 : IL^3

o5 = image | a b 0 0 0 0 |
           | 0 0 a b 0 0 |
           | 0 0 0 0 a b |

                                         3
o5 : coherent sheaf on Q, subsheaf of OO
                                        Q

See also

Proj -- make a projective variety
sheaf -- make a coherent sheaf

Ways to use this method:

CoherentSheaf ^ ZZ -- direct sum
SheafOfRings ^ ZZ