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families -- outputs the perturbed families of a NestedDeformation

Description

The first element of S is the family for subscheme/quotient module, and the second element is the family for the ambient scheme or module.

i1 : R=QQ[x,y];
i2 : F0Y=basis(3,R);

             1      4
o2 : Matrix R  <-- R
i3 : F0X=basis(2,R);

             1      3
o3 : Matrix R  <-- R
i4 : D=nestedHilbertScheme(F0X,F0Y);
i5 : transpose (families D)_0

o5 = {-2} | t_2t_3-t_3^2-t_1t_4+t_1t_5+yt_1+xt_2+x2  |
     {-2} | t_3t_4-t_1t_6+yt_3+xt_4+xy               |
     {-2} | -t_4^2+t_4t_5+t_2t_6-t_3t_6+yt_5+xt_6+y2 |

                        3                 1
o5 : Matrix (R[t ..t  ])  <-- (R[t ..t  ])
                1   18            1   18
i6 : transpose (families D)_1

o6 = {-3} | t_9t_11t_13-t_11^2t_13-t_8t_12t_13+t_10t_12t_13-t_9t_13^2+t
     {-3} | t_11t_12t_13-t_12t_13^2-t_10t_12t_14-t_8t_13t_15+t_10t_13t_
     {-3} | -t_12^2t_13+t_12t_13t_14+t_10t_12t_15+t_9t_13t_15-t_11t_13t
     {-3} | t_12^2t_14-t_12t_14^2-t_11t_12t_15+t_12t_13t_15-t_9t_14t_15
     ------------------------------------------------------------------------
     _11t_13^2-t_9t_10t_14+t_10t_11t_14+t_7t_12t_14+t_8t_13t_14-t_10t_13t_14-
     15+t_7t_14t_15+t_10t_12t_16-t_7t_15t_16+t_8t_10t_18-t_10^2t_18-t_7t_11t_
     _15-t_7t_15^2-t_10t_12t_17+t_7t_15t_17-t_9t_10t_18+t_10t_11t_18+t_7t_12t
     +t_11t_14t_15+t_8t_15^2-t_10t_15^2-t_12^2t_16+t_12t_14t_16+t_9t_15t_16-t
     ------------------------------------------------------------------------
     t_7t_14^2+t_8t_10t_15-t_10^2t_15-t_7t_11t_15+t_7t_13t_15+t_9t_10t
     18+t_7t_13t_18+yt_10t_12+xt_11t_12+yt_11t_13-yt_13^2-yt_10t_14-yt
     _18-t_7t_14t_18-xt_12^2+xt_12t_14+yt_13t_14+xt_9t_15+yt_10t_15-xt
     _11t_15t_16+t_11t_12t_17-t_12t_13t_17-t_8t_15t_17+t_10t_15t_17+t_
     ------------------------------------------------------------------------
     _16-t_10t_11t_16-t_7t_12t_16+t_7t_14t_16-t_8t_10t_17+t_10^2t_17+t_7t_11t
     _7t_15-xt_8t_15+xt_10t_15+yt_10t_16-xt_7t_18+y2t_10+xyt_11+x2t_12+x2y   
     _11t_15+xt_13t_15-yt_10t_17-yt_7t_18-xt_10t_18+y2t_13+xyt_14+x2t_15+xy2 
     9t_11t_18-t_11^2t_18-t_8t_12t_18+t_10t_12t_18-t_9t_13t_18+t_11t_13t_18+t
     ------------------------------------------------------------------------
     _17-t_7t_13t_17+yt_9t_10+xt_9t_11-yt_10t_11-xt_11^2-yt_7t_12-xt_8t_12+xt
                                                                             
                                                                             
     _8t_14t_18-t_10t_14t_18-yt_12^2+yt_12t_14-yt_14^2+yt_9t_15-2yt_11t_15-xt
     ------------------------------------------------------------------------
     _10t_12+yt_8t_13-yt_10t_13+xt_11t_13-xt_13^2+xt_8t_14-2xt_10t_14-xt_7t_
                                                                            
                                                                            
     _12t_15+yt_13t_15-xt_14t_15+yt_14t_16+xt_15t_16+yt_11t_17+xt_12t_17-yt_
     ------------------------------------------------------------------------
     15+yt_7t_16+xt_10t_16+xt_7t_17+y2t_7+xyt_8+x2t_9+x3                  |
                                                                          |
                                                                          |
     13t_17+yt_8t_18+xt_9t_18-yt_10t_18-xt_13t_18+y2t_16+xyt_17+x2t_18+y3 |

                        4                 1
o6 : Matrix (R[t ..t  ])  <-- (R[t ..t  ])
                1   18            1   18

Ways to use families:

  • families(NestedDeformation)

For the programmer

The object families is a method function.


The source of this document is in VersalDeformations.m2:1978:0.