fanoFourfold -- random prime Fano fourfold of coindex at most 3

Synopsis

• Usage:

  fanoFourfold(d,g)

  fanoFourfold(d,g,CoefficientRing=>K)

• Inputs:
  • (d,g) a pair of integers belonging to the set $\{(2,0),(3,1),(4,1),(5,1),(4,3),(6,4),(8,5),(10,6),(12,7),(14,8),(16,9),(18,10)\}$
• Optional inputs:
  • CoefficientRing => ..., default value ZZ/65521
• Outputs:
  • an embedded projective variety, a random prime Fano fourfold of coindex at most 3 having degree $d$ and genus $g$

Description

i1 : X = fanoFourfold(4,1);

o1 : ProjectiveVariety, 4-dimensional subvariety of PP^6

i2 : describe X

o2 = ambient:.............. PP^6
     dim:.................. 4
     codim:................ 2
     degree:............... 4
     generators:........... 2^2 
     purity:............... true
     dim sing. l.:......... -1

i3 : parametrize X

o3 = multi-rational map consisting of one single rational map
     source variety: PP^4
     target variety: 4-dimensional subvariety of PP^6 cut out by 2 hypersurfaces of degree 2
     dominance: true
     degree: 1

o3 : MultirationalMap (birational map from PP^4 to X)

See also

• parametrizeFanoFourfold -- rational parametrization of a prime Fano fourfold of coindex at most 3