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 = F

o1 : Fan

i2 : raysF = rays F

o2 = | 1 0  0 -1 |
     | 0 -1 1 3  |

              2        4
o2 : Matrix ZZ  <--- ZZ

i3 : apply(maxCones F, mc -> raysF_mc)

o3 = {| 1 0 |, | 0 -1 |, | 1 0  |, | 0  -1 |}
      | 0 1 |  | 1 3  |  | 0 -1 |  | -1 3  |

o3 : List