specialGushelMukaiFourfold(String,Ring) -- random special Gushel-Mukai fourfold of a given type

Synopsis

Function: specialGushelMukaiFourfold
Usage:

specialGushelMukaiFourfold(n,K)

specialGushelMukaiFourfold n
Inputs:
- n, a string, the name of some known type of Gushel-Mukai fourfolds
- K, a ring, the coefficient ring
Optional inputs:
- InputCheck => ..., default value 1, make a special Gushel-Mukai fourfold
- Verbose => ..., default value false, request verbose feedback
Outputs:
- a special Gushel-Mukai fourfold, a random special Gushel-Mukai fourfold of the indicated type over K

Description

i1 : X = specialGushelMukaiFourfold("cubic scroll",ZZ/65521);

o1 : ProjectiveVariety, GM fourfold containing a surface of degree 3 and sectional genus 0

i2 : describe X

o2 = Special Gushel-Mukai fourfold of discriminant 12
     containing a surface in PP^8 of degree 3 and sectional genus 0
     cut out by 7 hypersurfaces of degrees (1,1,1,1,2,2,2)
     and with class in G(1,4) given by 2*s_(3,1)+s_(2,2)
     Type: ordinary
     (case 7 of Table 1 in arXiv:2002.07026)

References

O. Debarre, A. Iliev, and L. Manivel, Special prime Fano fourfolds of degree 10 and index 2, available at arXiv:1302.1398 (2014).
G. Staglianò, On some families of Gushel-Mukai fourfolds, available at arXiv:2002.07026 (2020).

Ways to use this method: