SumOfTwists -- the class of all sums of twists

Description

This class is used internally as an abstract representation of a graded module as an infinite direct sum of twists of a coherent sheaf.

i1 : R = QQ[x,y,z]

o1 = R

o1 : PolynomialRing

i2 : X = Proj R

o2 = X

o2 : ProjectiveVariety

i3 : OO_X(*)

        1
o3 = OO   (*)
       X

o3 : SumOfTwists

i4 : peek oo

                    1
o4 = SumOfTwists{OO  , LowerBound{-infinity}}
                   X

i5 : OO_X(>=2)

        1
o5 = OO  (>= 2)
       X

o5 : SumOfTwists

i6 : peek oo

                    1
o6 = SumOfTwists{OO  , LowerBound{2}}
                   X

i7 : Ext^0(OO_X^1, OO_X^1)

       1
o7 = QQ

o7 : QQ-module, free

i8 : Ext^0(OO_X^1, OO_X^1(*))

      1
o8 = R

o8 : R-module, free

CoherentSheaf (*) -- sum of twists
SheafOfRings (*) -- see CoherentSheaf (*) -- sum of twists
CoherentSheaf LowerBound -- see LowerBound -- the class of lower bound objects
SheafOfRings LowerBound -- see LowerBound -- the class of lower bound objects

expression(SumOfTwists) (missing documentation)
Ext^ZZ(CoherentSheaf,SumOfTwists) -- global Ext
Ext^ZZ(SheafOfRings,SumOfTwists) -- see Ext^ZZ(CoherentSheaf,SumOfTwists) -- global Ext
HH^ZZ SumOfTwists -- coherent sheaf cohomology module
HH^ZZ(ProjectiveVariety,SumOfTwists) -- see HH^ZZ SumOfTwists -- coherent sheaf cohomology module
isLocallyFree(SumOfTwists) -- see isLocallyFree -- whether a coherent sheaf is locally free
net(SumOfTwists) (missing documentation)
ring(SumOfTwists) -- see ring(CoherentSheaf) -- the coordinate ring of the underlying variety
texMath(SumOfTwists) (missing documentation)
toString(SumOfTwists) (missing documentation)
variety(SumOfTwists) -- see variety(CoherentSheaf) -- the underlying variety over which a coherent sheaf or morphism is defined.

The object SumOfTwists is a type, with ancestor classes BasicList < Thing.

The source of this document is in Varieties/doc-sheaves.m2:80:0.