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AFPVariety -- non-equivariantly formal toric varieties

Description

Normal toric variety whose equivariant cohomology is not free but is torsion-free (as described in https://doi.org/10.1090/S0002-9947-2014-06165-5). These varieties are described by their complex dimension $d$, and the syzygy order $ord$ of their equivariant cohomology. Note that we must have 1 < ord < d. For ord = 0, the equivariant cohomology is not torsion-free and for ord = d, the equivariant cohomology is free. So we don't handle those cases. The variety is obtained by removing two appropriately chosen fixed points from $(\mathbb{CP}^1)^d$.

The AFPVarity(2, 1) is $(\mathbb{CP^1})^2 - \{([1:0], [1:0]), ([0:1], [0:1])\}$.

i1 : X = AFPVariety (2, 1)

o1 = X

o1 : NormalToricVariety
i2 : betti X

o2 = {1, 0, 2, 1, 0}

o2 : List

Ways to use AFPVariety:

  • AFPVariety(ZZ,ZZ)

For the programmer

The object AFPVariety is a method function.


The source of this document is in ToricTopology/Documentation.m2:644:0.