symmetricUniversalFamily -- Build the miniversal deformation over V(n)

Synopsis

Usage:
(J2,I2)=symmetricUniversalFamily(n,phi,J,I)
Inputs:
- n, an integer, the number of variables of the homogeneous coordinate ring of P^n-1
- phi, a ring map, from A to Asym
- J, an ideal, flattening relation in A
- I, an ideal, of the universal unfolding in P^n-1 x Spec A
Outputs:
- J2, an ideal, flattening relation in the minimal base ring B
- I2, an ideal, defining the universal family in P^n-1 x Spec B

Description

Construct the minimal base ring B, the flattening relations in B, and the universal flat family defined by I2 in P^n-1 x Spec(B/J2)

i1 : p=0,n=4

o1 = (0, 4)

o1 : Sequence

i2 : (R,A,I)=unfoldingEquations(p,n);

i3 : time (lin,J0)=equationsInThePaper(n,A);betti J0
     -- used 0.00523277 seconds

            0  1
o4 = total: 1 12
         0: 1  2
         1: .  5
         2: .  4
         3: .  1

o4 : BettiTally

i5 : (Asym,phi)=symmetryMap(n,A);

i6 : (J2,I2)=symmetricUniversalFamily(n,phi,J0,I);

i7 : betti J2

            0
o7 = total: 1
         0: 1

o7 : BettiTally

i8 : I2

             2        3                                     2            
o8 = ideal (x  - x x a      + x x a     a     a      + x x a     a      -
             1    3 4 2,2,3    3 4 2,2,2 2,2,3 2,3,3    2 4 2,2,3 2,3,3  
     ------------------------------------------------------------------------
                2                  2        2 2     2            3      
     x x a     a      - x x a     a      - x a     a      + x x a      +
      2 4 2,2,2 2,3,3    3 4 2,2,3 2,3,3    4 2,2,3 2,3,3    2 4 2,3,3  
     ------------------------------------------------------------------------
      2       3        2 4            2              2 3            
     x a     a      - x a      + x x a     a      + x a     a      -
      4 2,2,2 2,3,3    4 2,3,3    3 4 2,2,3 3,3,3    4 2,2,3 3,3,3  
     ------------------------------------------------------------------------
                               2                          
     x x a     a     a      - x a     a     a     a      +
      2 4 2,2,3 2,3,3 3,3,3    4 2,2,2 2,2,3 2,3,3 3,3,3  
     ------------------------------------------------------------------------
       2       2              2 2     2                  2      
     2x a     a     a      - x a     a     , x x  - x x a      +
       4 2,2,3 2,3,3 3,3,3    4 2,2,3 3,3,3   1 2    2 4 2,2,3  
     ------------------------------------------------------------------------
                         2 2                  2        2       2      
     x x a     a      + x a     a      - x x a      - x a     a      +
      2 4 2,2,2 2,3,3    4 2,2,3 2,3,3    2 4 2,3,3    4 2,2,2 2,3,3  
     ------------------------------------------------------------------------
      2 3                           2                            2 3      
     x a      + x x a     a      - x a     a     a     , x x  - x a      +
      4 2,3,3    2 4 2,2,3 3,3,3    4 2,2,3 2,3,3 3,3,3   1 3    4 2,2,3  
     ------------------------------------------------------------------------
      2                      2       2        2 2             2         
     x a     a     a      - x a     a      + x a     a     , x  - x x  -
      4 2,2,2 2,2,3 2,3,3    4 2,2,3 2,3,3    4 2,2,3 3,3,3   2    1 4  
     ------------------------------------------------------------------------
                                2 2        2                2 2      
     x x a      - x x a      - x a      + x a     a      - x a      +
      2 4 2,2,2    3 4 2,2,3    4 2,2,3    4 2,2,2 2,3,3    4 2,3,3  
     ------------------------------------------------------------------------
      2                                               2
     x a     a     , x x  - x x a      - x x a     , x  - x x  - x x a      -
      4 2,2,3 3,3,3   2 3    2 4 2,2,3    3 4 2,3,3   3    1 4    2 4 2,3,3  
     ------------------------------------------------------------------------
     x x a     )
      3 4 3,3,3

o8 : Ideal of QQ[x , x , x , x , a     , a     , a     , a     ]
                  1   2   3   4   2,2,2   2,2,3   2,3,3   3,3,3

i9 : isHomogeneous I2

o9 = true

Ways to use `symmetricUniversalFamily` :

symmetricUniversalFamily(ZZ,RingMap,Ideal,Ideal) (missing documentation)

symmetricUniversalFamily -- Build the miniversal deformation over V(n)

Synopsis

Description

Ways to use symmetricUniversalFamily :

Ways to use `symmetricUniversalFamily` :