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NormalToricVarieties :: id _ NormalToricVariety

id _ NormalToricVariety -- make the identity map from a NormalToricVariety to itself

Synopsis

Description

For the identity map on a normal toric variety, the underlying map of lattices is given by the identity matrix. For more information on this correspondence, see Theorem 3.3.4 in Cox-Little-Schenck's Toric Varieties.

i1 : X = hirzebruchSurface 2;
i2 : f = id_X

o2 = | 1 0 |
     | 0 1 |

o2 : ToricMap X <--- X
i3 : assert (isWellDefined f and source f === X and
         target f === X and matrix f === id_(ZZ^(dim X)))

Identity maps also arise as edge cases of the canonical projections and inclusions associated to Cartesian products.

i4 : X2 = X ** X;
i5 : X2^[0,1]

o5 = | 1 0 0 0 |
     | 0 1 0 0 |
     | 0 0 1 0 |
     | 0 0 0 1 |

o5 : ToricMap X2 <--- X2
i6 : X2_[0,1]

o6 = | 1 0 0 0 |
     | 0 1 0 0 |
     | 0 0 1 0 |
     | 0 0 0 1 |

o6 : ToricMap X2 <--- X2
i7 : assert (X2^[0,1] == id_X2 and X2_[0,1] == id_X2)

See also