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DefParam -- deformation parameter

Description

DefParam, DefParamX, DefParamY are the names of optional arguments. Their value are a symbol, which specifies the name of the deformation parameter. Their default values is determined by the loadtime configuration Option DefaultDefParam,DelfaultDefParamX,DefaultDefParamY, which have default values t,s,t.

For example, we may use the deformation parameter s:

i1 : S=QQ[x_0..x_4];
 
i2 : I=minors(2,matrix {{x_0,x_1,x_2,x_3},{x_1,x_2,x_3,x_4}});

o2 : Ideal of S
 
i3 : F0=gens I

o3 = | -x_1^2+x_0x_2 -x_1x_2+x_0x_3 -x_2^2+x_1x_3 -x_1x_3+x_0x_4
     ------------------------------------------------------------------------
     -x_2x_3+x_1x_4 -x_3^2+x_2x_4 |

             1      6
o3 : Matrix S  <-- S
 
i4 : (F,R,G,C)=versalDeformation(F0,DefParam=>s);
 
i5 : sum F

o5 = | x_1s_1+x_0s_2-x_1^2+x_0x_2 -s_1s_3+x_0s_4-x_1x_2+x_0x_3
     ------------------------------------------------------------------------
     -s_2s_3+s_3^2-s_1s_4-x_3s_1-x_2s_2+x_1s_4-x_2^2+x_1x_3
     ------------------------------------------------------------------------
     s_2s_3-s_3^2+x_2s_3-x_1x_3+x_0x_4 -x_4s_1-x_3s_2+x_3s_3-x_2x_3+x_1x_4
     ------------------------------------------------------------------------
     x_4s_3-x_3s_4-x_3^2+x_2x_4 |

                       1                6
o5 : Matrix (S[s ..s ])  <-- (S[s ..s ])
                1   4            1   4

See also

Functions with optional argument named DefParam:

  • versalDeformation(Matrix,DefParam=>...)
  • versalDeformation(Matrix,Matrix,Matrix,DefParam=>...)
  • firstOrderDeformations(...,DefParam=>...) -- see firstOrderDeformations -- use tangent space to create first order perturbations and find relations
  • localHilbertScheme(...,DefParam=>...) -- see localHilbertScheme -- computes a power series representation of the local Hilbert scheme

For the programmer

The object DefParam is a symbol.

The source of this document is in VersalDeformations.m2:2034:0.