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Target SSM multi-singularity Thom polynomials for l=5

Target SSM multi -singularity Thom polynomials of contact multi -singularities of relative dimension 5

codimension 0

codimension 1

codimension 2

codimension 3

codimension 4

codimension 5

  • Target SSM multisingularity Thom polynomial in monomial basis:

    • +t^5*( s[[]] )
    +t^6*( -s[[1]] )
    +t^7*( -s[[2]] +s[[1,1]] )
    +t^8*( -s[[3]] +2*s[[1,2]] -s[[1,1,1]] )
    +t^9*( -s[[4]] +2*s[[1,3]] +s[[2,2]] -3*s[[1,1,2]] +s[[1,1,1,1]] )
    +t^10*( 2*s[[1,4]] +2*s[[2,3]] -3*s[[1,1,3]] -3*s[[1,2,2]] +4*s[[1,1,1,2]] -s[[1,1,1,1,1]] )
    +t^11*( -7*s[[6]] +2*s[[2,4]] +s[[3,3]] -3*s[[1,1,4]] -6*s[[1,2,3]] -s[[2,2,2]] +4*s[[1,1,1,3]] +6*s[[1,1,2,2]] -5*s[[1,1,1,1,2]] +s[[1,1,1,1,1,1]] )
    +t^12*( 19*s[[7]] +15*s[[1,6]] +2*s[[3,4]] -6*s[[1,2,4]] -3*s[[1,3,3]] -3*s[[2,2,3]] +4*s[[1,1,1,4]] +12*s[[1,1,2,3]] +4*s[[1,2,2,2]] -5*s[[1,1,1,1,3]] -10*s[[1,1,1,2,2]] +6*s[[1,1,1,1,1,2]] -s[[1,1,1,1,1,1,1]] )

    codimension 6

    codimension 7

    codimension 8

    codimension 9

    codimension 10

  • Target SSM multisingularity Thom polynomial in monomial basis:

    • +t^10*( -s[[5]] )
    +t^11*( 5*s[[6]] +2*s[[1,5]] )
    +t^12*( -15*s[[7]] -11*s[[1,6]] +2*s[[2,5]] -3*s[[1,1,5]] )

    codimension 11

  • Target SSM multisingularity Thom polynomial in monomial basis:

    • +t^11*( s[[6]] )
    +t^12*( -5*s[[7]] -2*s[[1,6]] )

    codimension 12