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SpecialFanoFourfolds :: GMtables

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

Synopsis

Description

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

                                            2                              
o1 = (ideal (x , x x  - x x , x x  - x x , x  - x x ), ideal (x  - 8610x  +
              5   2 3    1 4   1 3    0 4   1    0 2           1        2  
     ------------------------------------------------------------------------
                                                                        
     10298x  - 14788x , x  - 3956x  + 10298x  + 5320x  - 13137x , x x  -
           4         5   0        2         3        4         5   2 3  
     ------------------------------------------------------------------------
                      2                                            2        
     8610x x  + 10298x  + 10259x x  - 11729x x  + 13696x x  + 7509x ), ideal
          2 4         4         2 5         3 5         4 5        5        
     ------------------------------------------------------------------------
                                                                       
     (x , x  - 8610x  + 10298x , x  - 3956x  + 10298x  + 5320x , x x  -
       5   1        2         4   0        2         3        4   2 3  
     ------------------------------------------------------------------------
                      2
     8610x x  + 10298x ))
          2 4         4

o1 : Sequence
i2 : (?B,?V,?C)

o2 = (smooth cubic surface in PP^5 cut out by 4 hypersurfaces of degrees
     ------------------------------------------------------------------------
     (1,2,2,2), smooth quadric surface in PP^5, irreducible conic curve in
     ------------------------------------------------------------------------
     PP^5)

o2 : Sequence
i3 : B + V == C

o3 = true

The corresponding example of fourfold can be obtained as follows.

i4 : psi = rationalMap(B,Dominant=>2);

o4 : RationalMap (quadratic rational map from PP^5 to 5-dimensional subvariety of PP^8)
i5 : X = specialGushelMukaiFourfold psi V;

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

This is basically the same as doing this:

i6 : specialGushelMukaiFourfold("1",ZZ/33331);

o6 : ProjectiveVariety, GM fourfold containing a surface of degree 2 and sectional genus 0

See also

Ways to use GMtables :

For the programmer

The object GMtables is a method function.