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Macaulay2Doc :: SheafOfRings ^ List

SheafOfRings ^ List -- make a graded free coherent sheaf

Synopsis

Description

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

o1 = R

o1 : QuotientRing
i2 : X = Proj R

o2 = X

o2 : ProjectiveVariety
i3 : OO_X^{-1,-2,3}

        1           1           1
o3 = OO  (-1) ++ OO  (-2) ++ OO  (3)
       X           X           X

o3 : coherent sheaf on X, free

If i, j, ... are lists of integers, then they represent multi-degrees, as in graded and multigraded polynomial rings.

i4 : Y = Proj (QQ[x,y,z,Degrees=>{{1,0},{1,-1},{1,-2}}])

o4 = Y

o4 : ProjectiveVariety
i5 : OO_Y^{{1,2},{-1,3}}

        1              1
o5 = OO   (1, 2) ++ OO   (-1, 3)
       Y              Y

o5 : coherent sheaf on Y, free
i6 : degrees oo

o6 = {{-1, -2}, {1, -3}}

o6 : List

See also