hirzebruch -- computes the fan of the r-th Hirzebruch surface

Synopsis

• Usage:

  F = hirzebruch r

• Inputs:
  • r, an integer, positive
• Outputs:
  • F, an instance of the type Fan

Description

The r-th Hirzebruch surface is the Fan in QQ^2 generated by the cones <e_1,e_2>, <e_1,-e_2>, <-e_1+r*e_2,-e_2> and <-e_1+r*e_2,e_2>.

i1 : F = hirzebruch 3

o1 = {ambient dimension => 2         }
      number of generating cones => 4
      number of rays => 4
      top dimension of the cones => 2

o1 : Fan

i2 : apply(maxCones F,rays)

o2 = {| 1 0  |, | 0  -1 |, | 0 -1 |, | 1 0 |}
      | 0 -1 |  | -1 3  |  | 1 3  |  | 0 1 |

o2 : List