GMtables -- make examples of reducible subschemes of P^5

Usage:

GMtables(i,K)
Inputs:
- i, an integer, an integer between 1 and 21
- K, a ring, the coefficient ring
Optional inputs:
- Verify => ..., default value true
Outputs:
- a triple of varieties, $(B,V,C)$, which represents a reducible subscheme of $\mathbb{P}^5$, in accordance with the 21 examples listed in Table 2 of the paper On some families of Gushel-Mukai fourfolds.

Description

i1 : (B,V,C) := GMtables(1,ZZ/33331)

o1 = (surface in PP^5 cut out by 4 hypersurfaces of degrees 1^1 2^3 , surface
     ------------------------------------------------------------------------
     in PP^5 cut out by 3 hypersurfaces of degrees 1^2 2^1 , curve in PP^5
     ------------------------------------------------------------------------
     cut out by 4 hypersurfaces of degrees 1^3 2^1 )

o1 : Sequence

i2 : B * V == C

o2 = true

The corresponding example of fourfold reported in Table 1 of the aforementioned paper can be obtained as follows.

i3 : psi = rationalMap(ideal B,Dominant=>2);

o3 : RationalMap (quadratic rational map from PP^5 to 5-dimensional subvariety of PP^8)

i4 : X = gushelMukaiFourfold psi ideal V;

o4 : ProjectiveVariety, GM fourfold containing a surface of degree 2 and sectional genus 0

This is basically the same as doing this:

i5 : gushelMukaiFourfold("1",ZZ/33331);

o5 : ProjectiveVariety, GM fourfold containing a surface of degree 2 and sectional genus 0

Ways to use GMtables:

GMtables(ZZ)
GMtables(ZZ,Ring)

For the programmer

The object GMtables is a method function with options.

The source of this document is in /__w/M2/M2/macaulay2-1.26.05+ds/M2/Macaulay2/packages/SpecialFanoFourfolds/docs.m2:115:0.

GMtables -- make examples of reducible subschemes of P^5

Description

See also

Ways to use GMtables:

For the programmer