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toricLL -- computes the BGG functor of a module over the Koszul dual exterior algebra of a multigraded polynomial ring

Synopsis

Description

Given a multigraded polynomial ring $S$ with Koszul dual exterior algebra E, the BGG functor $\mathbf{L}$ sends an $E$-module to a linear complex of $S$-modules.

i1 : S = ring hirzebruchSurface 3

o1 = S

o1 : PolynomialRing
i2 : E = dualRingToric S

o2 = E

o2 : PolynomialRing, 4 skew commutative variable(s)
i3 : C = toricLL(coker matrix{{e_0, e_1}})

                 1                 2                 1
o3 = (QQ[x ..x ])  <-- (QQ[x ..x ])  <-- (QQ[x ..x ])
          0   3             0   3             0   3
                                          
     -2                -1                0

o3 : Complex

See also

Ways to use toricLL :

For the programmer

The object toricLL is a method function.