Tp’s, l=0
Thom polynomials of contact singularities of relative dimension 0
(Hierarchy of these singularities)
codimension 0
| Local algebra | C |
| Thom-Boardman class | \Sigma^0 |
| Codimension | 0 |
| Thom polynomial in Chern classes | 1 |
| Thom polynomial in Schur functions | 1 |
| Remarks |
This contact singularity is open in its Thom-Boardman class. Source: Implicit function theorem. |
codimension 1
| Local algebra | C[x]/(x^2) |
| Thom-Boardman class | \Sigma^{1,0} |
| Codimension | 1 |
| Thom polynomial in Chern classes | c_1 |
| Thom polynomial in Schur functions | s_1 |
| Remarks |
This contact singularity is open in its Thom-Boardman class. Source: I. Porteous: Simple singularities of maps. In Proc. Liverpool Singularities I, Springer LNM 192 (1971), 268-307 |
codimension 2
| Local algebra | C[x]/(x^3) |
| Thom-Boardman class | \Sigma^{1,1,0} |
| Codimension | 2 |
| Thom polynomial in Chern classes | c_1^2+ c_2 |
| Thom polynomial in Schur functions | s_{1,1}+ 2s_{2} |
| Remarks |
This contact singularity is open in its Thom-Boardman class. Source: F. Ronga: Le calcul des classes duales aux singularités de Boardman d’ordre deux, Commentarii mathematici Helvetici (1972), Vol. 47, 15-35 |
codimension 3
| Local algebra | C[x]/(x^4) |
| Thom-Boardman class | \Sigma^{1,1,1,0} |
| Codimension | 3 |
| Thom polynomial in Chern classes | c_1^3+ 3c_1c_2+ 2c_3 |
| Thom polynomial in Schur functions | s_{1,1,1}+ 5s_{2,1}+ 6s_{3} |
| Remarks | This contact singularity is open in its Thom-Boardman class. |
codimension 4
| Local algebra | C[x]/(x^5) |
| Thom-Boardman class | \Sigma^{1,1,1,1,0} |
| Codimension | 4 |
| Thom polynomial in Chern classes | c_1^4+ 6c_1^2c_2+ 2c_2^2+ 9c_1c_3+ 6c_4 |
| Thom polynomial in Schur functions | s_{1,1,1,1}+ 9s_{2,1,1}+ 10s_{2,2}+ 26s_{3,1}+ 24s_{4} |
| Remarks |
This contact singularity is open in its Thom-Boardman class. T. Gaffney: The Thom polynomial of  . Singularities, Part 1 (Arcata, Calif., 1981), 399-408, Proc. Sympos.. Pure Math., 40, AMS, Providence RI, 1983This was the first known Thom polynomial whose calculation required consideration of non-Morin singularities. Warning: This Thom polynomial is wrongly quoted in V. A. Vassiliev, V. Arnold, V. Goryunov, O. Lyashko: Dynamical Systems VI. Singularity Theory I. Encyclopaedia of Math. Sciences Vol. 6, Springer 1993 |
| Local algebra | C[x,y]/(x^2,y^2) |
| Thom-Boardman class | \Sigma^{2,0} |
| Codimension | 4 |
| Thom polynomial in Chern classes | c_2^2-c_1c_3 |
| Thom polynomial in Schur functions | s_{2,2} |
| Remarks |
This contact singularity is open in its Thom-Boardman class. Source: I. Porteous: Simple singularities of maps. In Proc. Liverpool Singularities I, Springer LNM 192 (1971), 268-307 |
codimension 5
| Local algebra | C[x]/(x^6) |
| Thom-Boardman class | \Sigma^{1,1,1,1,1,0} |
| Codimension | 5 |
| Thom polynomial in Chern classes | c_1^5+ 10c_1^3c_2+ 25c_1^2c_3+ 10c_1c_2^2+ 38c_1c_4+ 12c_2c_3+ 24c_5 |
| Thom polynomial in Schur functions | s_{1,1,1,1,1}+ 14s_{2,1,1,1}+ 35s_{2,2,1}+ 71s_{3,1,1}+ 92s_{3,2}+ 154s_{4,1}+ 120s_{5} |
| Remarks |
This contact singularity is open in its Thom-Boardman class. Source: R. Turnball: The Thom-Boardman singularities $\Sigma^1$, $\Sigma^{1,1}$, $\Sigma^{1,1,1}$, $\Sigma^{1,1,1,1}$, $\Sigma^{1,1,1,1,1}$ and their closures. Ph D. Thesis, Liverpool University 1989 |
| Local algebra | C[x,y]/(xy,x^2+y^3) |
| Thom-Boardman class | \Sigma^{2,0} |
| Codimension | 5 |
| Thom polynomial in Chern classes | 2c_1c_2^2-2c_1^2c_3+ 2c_2c_3-2c_1c_4 |
| Thom polynomial in Schur functions | 2s_{2,2,1}+ 4s_{3,2} |
| Remarks |
Source: I. Porteous: The second-order decomposition of  , Topology, Vol 11 (1972), 325-334
|
codimension 6
| Local algebra | C[x]/(x^7) |
| Thom-Boardman class | \Sigma^{1,1,1,1,1,1,0} |
| Codimension | 6 |
| Thom polynomial in Chern classes | c_1^6+ 15c_1^4c_2+ 55c_1^3c_3+ 30c_1^2c_2^2+ 141c_1^2c_4+ 79c_1c_2c_3+ 5c_2^3+ 202c_1c_5+ 55c_2c_4+ 17c_3^2+ 120c_6 |
| Thom polynomial in Schur functions | s_{1,1,1,1,1,1}+ 20s_{2,1,1,1,1}+ 84s_{2,2,1,1}+ 70s_{2,2,2}+ 155s_{3,1,1,1}+ 455s_{3,2,1}+ 266s_{3,3}+ 580s_{4,1,1}+ 770s_{4,2}+ 1044s_{5,1}+ 720s_{6} |
| Remarks | Source: R. Rimanyi: Thom polynomials, symmetries and incidences of singularities; Inv. Math. 143, 499-521 (2001) |
| Local algebra | C[x,y]/(xy,x^2+y^4) |
| Thom-Boardman class | \Sigma^{2,0} |
| Codimension | 6 |
| Thom polynomial in Chern classes | 2c_1^2c_2^2+ 3c_2^3-2c_1^3c_3+ 2c_1c_2c_3-3c_3^2-5c_1^2c_4+ 9c_2c_4 |
| Thom polynomial in Schur functions | 2s_{2,2,1,1}+ 5s_{2,2,2}+ 12s_{3,2,1}+ 4s_{3,3}+ 16s_{4,2}+ 6s_{5,1}+ 6s_{6} |
| Remarks | Source: R. Rimanyi: Thom polynomials, symmetries and incidences of singularities; Inv. Math. 143, 499-521 (2001) |
| Local algebra | C[x,y]/(xy,x^3+y^3) |
| Thom-Boardman class | \Sigma^{2,0} |
| Codimension | 6 |
| Thom polynomial in Chern classes | c_1^2c_2^2-c_2^3-c_1^3c_3+ 3c_1c_2c_3+ 3c_3^2-2c_1^2c_4-3c_2c_4 |
| Thom polynomial in Schur functions | s_{2,2,1,1}+ 3s_{3,2,1}+ 6s_{3,3}+ 2s_{4,2} |
| Remarks |
Source: I. Porteous: The second-order decomposition of , Topology, Vol 11 (1972), 325-334
|
codimension 7
| Local algebra | C[x]/(x^8) |
| Thom-Boardman class | \Sigma^{1,1,1,1,1,1,1,0} |
| Codimension | 7 |
| Thom polynomial in Chern classes | c_1^7+ 21c_1^5c_2+ 105c_1^4c_3+ 70c_1^3c_2^2+ 399c_1^3c_4+ 301c_1^2c_2c_3+ 35c_1c_2^3+ 960c_1^2c_5+ 467c_1c_2c_4+ 139c_1c_3^2+ 58c_2^2c_3+ 1284c_1c_6+ 326c_2c_5+ 154c_3c_4+ 720c_7 |
| Thom polynomial in Schur functions | s_{1,1,1,1,1,1,1}+ 27s_{2,1,1,1,1,1}+ 168s_{2,2,1,1,1}+ 294s_{2,2,2,1}+ 295s_{3,1,1,1,1}+ 1456s_{3,2,1,1}+ 1255s_{3,2,2}+ 1891s_{3,3,1}+ 1665s_{4,1,1,1}+ 4999s_{4,2,1}+ 3500s_{4,3}+ 5104s_{5,1,1}+ 6746s_{5,2}+ 8028s_{6,1}+ 5040s_{7} |
| Remarks | Source: R. Rimanyi: Thom polynomials, symmetries and incidences of singularities; Inv. Math. 143, 499-521 (2001) |
| Local algebra | C[x,y]/(xy,x^2+y^5) |
| Thom-Boardman class | \Sigma^{2,0} |
| Codimension | 7 |
| Thom polynomial in Chern classes | 2c_1^3c_2^2+ 9c_1c_3^2-2c_1^4c_3+ 14c_2^2c_3-17c_1c_3^2-9c_1^3c_4+ 29c_1c_2c_4-10c_3c_4-26c_1^2c_5+ 34c_2c_5-24c_1c_6 |
| Thom polynomial in Schur functions | 2s_{2,2,1,1,1}+ 13s_{2,2,2,1}+ 24s_{3,2,1,1}+ 47s_{3,2,2}+ 30s_{3,3,1}+ 82s_{4,2,1}+ 44s_{4,3}+ 84s_{5,2} |
| Remarks | Source: R. Rimanyi: Thom polynomials, symmetries and incidences of singularities; Inv. Math. 143, 499-521 (2001) |
| Local algebra | C[x,y]/(xy,x^3+y^4) |
| Thom-Boardman class | \Sigma^{2,0} |
| Codimension | 7 |
| Thom polynomial in Chern classes | 2c_1^3c_2^2-c_1c_2^3-2c_1^4c_3+ 8c_1^2c_2c_3-2c_2^2c_3+ 13c_1c_3^2-7c_1^3c_4-5c_1c_2c_4+ 10c_3c_4-6c_1^2c_5-10c_2c_5 |
| Thom polynomial in Schur functions | 2s_{2,2,1,1,1}+ 3s_{2,2,2,1}+ 13s_{3,2,1,1}+ 10s_{3,2,2}+ 32s_{3,3,1}+ s_{4,1,1,1}+ 26s_{4,2,1}+ 47s_{4,3}+ 3s_{5,1,1}+ 16s_{5,2}+ 3s_{6,1}+ s_{7} |
| Remarks | Source: R. Rimanyi: Thom polynomials, symmetries and incidences of singularities; Inv. Math. 143, 499-521 (2001) |
| Local algebra | C[x,y]/(x^2,y^3) |
| Thom-Boardman class | \Sigma^{2,1,0} |
| Codimension | 7 |
| Thom polynomial in Chern classes | 2c_1c_2^3-2c_1^2c_2c_3+ 2c_2^2c_3+ 2c_1c_3^2-4c_1c_2c_4+ 2c_3c_4-2c_2c_5 |
| Thom polynomial in Schur functions | s_{2,2,2,1}+ 2s_{3,2,1,1}+ 6s_{3,2,2}+ 6s_{3,3,1}+ 6s_{4,2,1}+ 8s_{4,3}+ 4s_{5,2} |
| Remarks |
Source: I. Porteous: The second-order decomposition of , Topology, Vol 11 (1972), 325-334 This contact singularity is open in its Thom-Boardman class. |
codimension 8
| Local algebra | C[x]/(x^9) |
| Thom-Boardman class | \Sigma^{1,1,1,1,1,1,1,1,0} |
| Codimension | 8 |
| Thom polynomial in Chern classes | c_{1}^8+ 28 c_{1}^6 c_{2}+ 140 c_{1}^4 c_{2}^2+ 140 c_{1}^2 c_{2}^3+ 14 c_{2}^4+ 182 c_{1}^5 c_{3}+ 868 c_{1}^3 c_{2} c_{3}+ 501 c_{1} c_{2}^2 c_{3}+ 642 c_{1}^2 c_{3}^2+ 202 c_{2} c_{3}^2+ 952 c_{1}^4 c_{4}+ 2229 c_{1}^2 c_{2} c_{4}+ 364 c_{2}^2 c_{4}+ 1559 c_{1} c_{3} c_{4}+ 332 c_{4}^2+ 3383 c_{1}^3 c_{5}+ 3455 c_{1} c_{2} c_{5}+ 954 c_{3} c_{5}+ 7552 c_{1}^2 c_{6}+ 2314 c_{2} c_{6}+ 9468 c_{1} c_{7}+ 5040 c_{8} |
| Thom polynomial in Schur functions | s_{1, 1, 1, 1, 1, 1, 1, 1}+ 35 s_{2, 1, 1, 1, 1, 1, 1}+ 300 s_{2, 2, 1, 1, 1, 1}+ 840 s_{2, 2, 2, 1, 1}+ 588 s_{2, 2, 2, 2}+ 511 s_{3, 1, 1, 1, 1, 1}+ 3732 s_{3, 2, 1, 1, 1}+ 6759 s_{3, 2, 2, 1}+ 8031 s_{3, 3, 1, 1}+ 8412 s_{3, 3, 2}+ 4025 s_{4, 1, 1, 1, 1}+ 20259 s_{4, 2, 1, 1}+ 17484 s_{4, 2, 2}+ 31584 s_{4, 3, 1}+ 12964 s_{4, 4}+ 18424 s_{5, 1, 1, 1}+ 54822 s_{5, 2, 1}+ 39764 s_{5, 3}+ 48860 s_{6, 1, 1}+ 63808 s_{6, 2}+ 69264 s_{7, 1}+ 40320 s_{8} |
| Remarks |
Source: R. Rimanyi: Thom polynomials, symmetries and incidences of singularities; Inv. Math. 143, 499-521 (2001) This contact singularity is open in its Thom-Boardman class. |
| Local algebra | C[x,y]/(xy,x^2+y^6) |
| Thom-Boardman class | \Sigma^{2,0} |
| Codimension | 8 |
| Thom polynomial in Chern classes | -120 c_{1} c_{7}+ 7 c_{2}^4-3 c_{4}^2+ 2 c_{1}^4 c_{2}^2-2 c_{1}^5 c_{3}-53 c_{1}^2 c_{3}^2+ 4 c_{2} c_{3}^2-14 c_{1}^4 c_{4}+ 74 c_{2}^2 c_{4}-71 c_{1}^3 c_{5}-39 c_{3} c_{5}-154 c_{1}^2 c_{6}+ 162 c_{2} c_{6}+ 60 c_{1}^2 c_{2} c_{4}-90 c_{1} c_{3} c_{4}+ 166 c_{1} c_{2} c_{5}+ 18 c_{1}^2 c_{2}^3-4 c_{1}^3 c_{2} c_{3}+ 57 c_{1} c_{2}^2 c_{3} |
| Thom polynomial in Schur functions | 2 s_{2, 2, 1, 1, 1, 1}+ 24 s_{2, 2, 2, 1, 1}+ 29 s_{2, 2, 2, 2}+ 40 s_{3, 2, 1, 1, 1}+ 194 s_{3, 2, 2, 1}+ 108 s_{3, 3, 1, 1}+ 194 s_{3, 3, 2}+ 250 s_{4, 2, 1, 1}+ 424 s_{4, 2, 2}+ 406 s_{4, 3, 1}+ 124 s_{4, 4}+ 620 s_{5, 2, 1}+ 412 s_{5, 3}+ 528 s_{6, 2} |
| Remarks | Source: R. Rimanyi: Thom polynomials, symmetries and incidences of singularities; Inv. Math. 143, 499-521 (2001) |
| Local algebra | C[x,y]/(xy,x^3+y^5) |
| Thom-Boardman class | \Sigma^{2,0} |
| Codimension | 8 |
| Thom polynomial in Chern classes | -4 c_{2}^4-20 c_{4}^2+ 2 c_{1}^4 c_{2}^2-2 c_{1}^5 c_{3}+ 13 c_{1}^2 c_{3}^2+ 24 c_{2} c_{3}^2-11 c_{1}^4 c_{4}-32 c_{2}^2 c_{4}-26 c_{1}^3 c_{5}+ 60 c_{3} c_{5}-24 c_{1}^2 c_{6}-40 c_{2} c_{6}+ 7 c_{1}^2 c_{2} c_{4}+ 34 c_{1} c_{3} c_{4}-2 c_{1} c_{2} c_{5}+ 3 c_{1}^2 c_{2}^3+ 8 c_{1}^3 c_{2} c_{3}+ 10 c_{1} c_{2}^2 c_{3} |
| Thom polynomial in Schur functions | 2 s_{2, 2, 1, 1, 1, 1}+ 9 s_{2, 2, 2, 1, 1}+ 3 s_{2, 2, 2, 2}+ 22 s_{3, 2, 1, 1, 1}+ 48 s_{3, 2, 2, 1}+ 66 s_{3, 3, 1, 1}+ 99 s_{3, 3, 2}+ 82 s_{4, 2, 1, 1}+ 75 s_{4, 2, 2}+ 232 s_{4, 3, 1}+ 76 s_{4, 4}+ 122 s_{5, 2, 1}+ 232 s_{5, 3}+ 60 s_{6, 2} |
| Remarks | Source: R. Rimanyi: Thom polynomials, symmetries and incidences of singularities; Inv. Math. 143, 499-521 (2001) |
| Local algebra | C[x,y]/(xy,x^4+y^4) |
| Thom-Boardman class | \Sigma^{2,0} |
| Codimension | 8 |
| Thom polynomial in Chern classes | -5 c_{1}^4 c_{4}+ 23 c_{4}^2+ 2 c_{2}^4+ 13 c_{2}^2 c_{4}+ c_{1}^4 c_{2}^2- c_{1}^5 c_{3}-11 c_{2} c_{3}^2-6 c_{1}^3 c_{5}-21 c_{3} c_{5}-2 c_{2} c_{6}+ 18 c_{1}^2 c_{3}^2-29 c_{1} c_{2} c_{5}- c_{1}^2 c_{2}^3-9 c_{1}^2 c_{2} c_{4}+ 27 c_{1} c_{3} c_{4}-5 c_{1} c_{2}^2 c_{3}+ 6 c_{1}^3 c_{2} c_{3} |
| Thom polynomial in Schur functions | s_{2, 2, 1, 1, 1, 1}+ 2 s_{2, 2, 2, 1, 1}+ 3 s_{2, 2, 2, 2}+ 8 s_{3, 2, 1, 1, 1}+ 15 s_{3, 2, 2, 1}+ 36 s_{3, 3, 1, 1}+ 21 s_{3, 3, 2}+ 23 s_{4, 2, 1, 1}+ 25 s_{4, 2, 2}+ 95 s_{4, 3, 1}+ 86 s_{4, 4}+ 28 s_{5, 2, 1}+ 62 s_{5, 3}+ 12 s_{6, 2} |
| Remarks | Source: R. Rimanyi: Thom polynomials, symmetries and incidences of singularities; Inv. Math. 143, 499-521 (2001) |
| Local algebra | C[x,y]/(x^2+y^3,xy^2) |
| Thom-Boardman class | \Sigma^{2,1} |
| Codimension | 8 |
| Thom polynomial in Chern classes | 2 c_{1}^2 c_{2}^3+ c_{2}^4-2 c_{1}^3 c_{2} c_{3}+ 4 c_{1} c_{2}^2 c_{3}+ 2 c_{1}^2 c_{3}^2+ 2 c_{2} c_{3}^2-7 c_{1}^2 c_{2} c_{4}+ 2 c_{2}^2 c_{4}+ 5 c_{1} c_{3} c_{4}+ c_{4}^2-9 c_{1} c_{2} c_{5}+ 3 c_{3} c_{5}-4 c_{2} c_{6} |
| Thom polynomial in Schur functions | 2 s_{2, 2, 2, 1, 1}+ 3 s_{2, 2, 2, 2}+ 2 s_{3, 2, 1, 1, 1}+ 15 s_{3, 2, 2, 1}+ 12 s_{3, 3, 1, 1}+ 21 s_{3, 3, 2}+ 12 s_{4, 2, 1, 1}+ 25 s_{4, 2, 2}+ 40 s_{4, 3, 1}+ 20 s_{4, 4}+ 22 s_{5, 2, 1}+ 32 s_{5, 3}+ 12 s_{6, 2} |
| Remarks | Source: R. Rimanyi: Thom polynomials, symmetries and incidences of singularities; Inv. Math. 143, 499-521 (2001) |
codimension 9
| Local algebra | C[x]/(x^{10}) |
| Thom-Boardman class | \Sigma^{1,1,1,1,1,1,1,1,1,0} |
| Codimension | 9 |
| Thom polynomial in Chern classes | 2421 c_3 c_2^2 c_1^2+ 2074 c_3^2 c_2 c_1+ 40320 c_9+ 8727 c_4 c_3 c_1^2+ 79344 c_8 c_1+ 18920 c_7 c_2+ 67076 c_7 c_1^2+ 29746 c_6 c_2 c_1+ 11726 c_5 c_3 c_1+ 7300 c_6 c_3+ 32244 c_6 c_1^3+ 4020 c_5 c_4+ 2940 c_5 c_2^2+ 9831 c_5 c_1^4+ 20123 c_5 c_2 c_1^2+ 2400 c_4 c_3 c_2+ 3856 c_4 c_2^2 c_1+ 7869 c_4 c_2 c_1^3+ 2100 c_3 c_2 c_1^4+ 4016 c_4^2 c_1+ 2016 c_4 c_1^5+ 220 c_3^3+ 2202 c_3^2 c_1^3+ 260 c_3 c_2^3+ 294 c_3 c_1^6+ 126 c_2^4 c_1+ 420 c_2^3 c_1^3+ 252 c_2^2 c_1^5+ 36 c_2 c_1^7+ c_1^9 |
| Thom polynomial in Schur functions | 174584 s_{4,3,2}+ 26115 s_{3,3,1, 1, 1}+ 149236 s_{4, 4,1}+ 54649 s_{5,1, 1, 1, 1}+ 271449 s_{5,2,1, 1}+ 232290 s_{5,2, 2}+ 455220 s_{6,3}+ 509004 s_{7,1, 1}+ 655824 s_{7,2}+ 663696 s_{8,1}+ 362880 s_{9}+ 437690 s_{5,3,1}+ 44 s_{2,1, 1, 1, 1, 1, 1, 1}+ 495 s_{2,2,1, 1, 1, 1, 1}+ 1980 s_{2,2,2,1, 1, 1}+ s_{1, 1, 1, 1, 1, 1, 1, 1, 1}+ 58346 s_{3,3,2,1}+ 23836 s_{3, 3, 3}+ 8624 s_{4,1, 1, 1, 1, 1}+ 64032 s_{4,2,1, 1, 1}+ 115766 s_{4, 2, 2, 1}+ 165354 s_{4,3,1, 1}+ 2772 s_{2, 2, 2, 2,1}+ 826 s_{3,1, 1, 1, 1, 1, 1}+ 8295 s_{3,2,1, 1, 1, 1}+ 218520 s_{5,4}+ 214676 s_{6,1, 1, 1}+ 627826 s_{6,2,1}+ 24003 s_{3,2,2,1, 1}+ 16919 s_{3,2, 2, 2} |
| Remarks |
This contact singularity is open in its Thom-Boardman class. Source: R. Rimanyi: unpublished |
| Local algebra | C[x,y]/(xy,x^2+y^7}) |
| Thom-Boardman class | \Sigma^{2,0} |
| Codimension | 9 |
| Thom polynomial in Chern classes | 18 c_5 c_3 c_1-22 c_6 c_2 c_1+ c_4 c_3 c_1^2-10 c_3^2 c_2 c_1-12 c_7 c_2+ 22 c_6 c_3-11 c_5 c_2 c_1^2-16 c_4 c_3 c_2+ 12 c_4 c_2^2 c_1-c_4 c_2 c_1^3-10 c_5 c_4+ 21 c_5 c_2^2-8 c_4^2 c_1+ 7 c_3^3+ 8 c_3 c_2^3-4 c_3 c_2^2 c_1^2+ 5 c_2^4 c_1 |
| Thom polynomial in Schur functions | 5 s_{2, 2, 2, 2,1}+ 11 s_{3,2,2,1, 1}+ 24 s_{3,2, 2, 2}+ 6 s_{3,3,1, 1, 1}+ 30 s_{3,3,2,1}+ 12 s_{3, 3, 3}+ 6 s_{4,2,1,1,1}+ 60 s_{4,2,2,1}+ 42 s_{4,3,1,1}+ 68 s_{4,3,2}+ 30 s_{4,4,1}+ 36 s_{5,2,1,1}+ 85 s_{5,2,2}+ 96 s_{5,3,1}+ 36 s_{5,4}+ 66 s_{6,2,1}+ 72 s_{6,3}+ 36 s_{7,2} |
| Remarks | Source: R. Rimanyi: unpublished |
| Local algebra | C[x,y]/(xy,x^4+y^5) |
| Thom-Boardman class | \Sigma^{2,0} |
| Codimension | 9 |
| Thom polynomial in Chern classes | 158 c_4 c_3 c_1^2-22 c_3^2 c_2 c_1-134 c_6 c_2 c_1-12 c_7 c_2-98 c_6 c_3-24 c_6 c_1^3+ 110 c_5 c_4+ 24 c_5 c_2^2-32 c_5 c_1^4-30 c_5 c_3 c_1-136 c_5 c_2 c_1^2+ 2 c_4 c_3 c_2+ 16 c_4 c_2^2 c_1-24 c_4 c_2 c_1^3-6 c_3 c_2^2 c_1^2+ 14 c_3 c_2 c_1^4+ 152 c_4^2 c_1-14 c_4 c_1^5+ 58 c_3^2 c_1^3+ 8 c_3 c_2^3-2 c_3 c_1^6-14 c_3^3+ 4 c_2^4 c_1+ 2 c_2^2 c_1^5 |
| Thom polynomial in Schur functions | 2 s_{2,2,1,1,1,1,1}+ 18 s_{2,2,2,1,1,1}+ 21 s_{2,2,2,2,1}+ 36 s_{3,2,1,1,1,1}+ 164 s_{3,2,2,1,1}+ 99 s_{3,2,2,2}+ 144 s_{3,3,1,1,1}+ 474 s_{3,3,2,1}+ 312 s_{3, 3, 3}+ 230 s_{4,2,1,1,1}+ 534 s_{4,2,2,1}+ 854 s_{4,3,1,1}+ 1192 s_{4,3,2}+ 716 s_{4,4,1}+ 660 s_{5,2,1,1}+ 652 s_{5,2,2}+ 1940 s_{5,3,1}+ 856 s_{5,4}+ 848 s_{6,2,1}+ 1552 s_{6,3}+ 384 s_{7,2} |
| Remarks | Source: R. Rimanyi: unpublished |
| Local algebra | C[x,y]/(x^2+y^3,y^4) |
| Thom-Boardman class | \Sigma^{2,1,0} |
| Codimension | 9 |
| Thom polynomial in Chern classes | -134 c_6 c_2 c_1-12 c_7 c_2-98 c_6 c_3-24 c_6 c_1^3+ 110 c_5 c_4+ 24 c_5 c_2^2-32 c_5 c_1^4-30 c_5 c_3 c_1-136 c_5 c_2 c_1^2+ 2 c_4 c_3 c_2+ 158 c_4 c_3 c_1^2+ 16 c_4 c_2^2 c_1-24 c_4 c_2 c_1^3-22 c_3^2 c_2 c_1-6 c_3 c_2^2 c_1^2+ 14 c_3 c_2 c_1^4+ 152 c_4^2 c_1-14 c_4 c_1^5+ 58 c_3^2 c_1^3+ 8 c_3 c_2^3-2 c_3 c_1^6-14 c_3^3+ 4 c_2^4 c_1+ 2 c_2^2 c_1^5 |
| Thom polynomial in Schur functions | 2 s_{2,2,1,1,1,1,1}+ 8 s_{2,2,2,1,1,1}+ 14 s_{2,2,2,2,1}+ 24 s_{3,2,1,1,1,1}+ 78 s_{3,2,2,1,1}+ 66 s_{3,2,2,2}+ 136 s_{3,3,1,1,1}+ 270 s_{3,3,2,1}+ 84 s_{3, 3, 3}+ 110 s_{4,2,1,1,1}+ 250 s_{4,2,2,1}+ 638 s_{4,3,1,1}+ 612 s_{4,3,2}+ 860 s_{4,4,1}+ 240 s_{5,2,1,1} |
| Remarks | Source: R. Rimanyi: unpublished |
| Local algebra | C[x,y]/(x^2+y^4,xy^2) |
| Thom-Boardman class | \Sigma^{2,1,0} |
| Codimension | 9 |
| Thom polynomial in Chern classes | 18 c_5 c_3 c_1-22 c_6 c_2 c_1+ c_4 c_3 c_1^2-10 c_3^2 c_2 c_1-12 c_7 c_2+ 22 c_6 c_3-11 c_5 c_2 c_1^2-16 c_4 c_3 c_2+ 12 c_4 c_2^2 c_1-c_4 c_2 c_1^3-10 c_5 c_4+ 21 c_5 c_2^2-8 c_4^2 c_1+ 7 c_3^3+ 8 c_3 c_2^3-4 c_3 c_2^2 c_1^2+ 5 c_2^4 c_1 |
| Thom polynomial in Schur functions | 5 s_{2,2,2,2,1}+ 11 s_{3,2,2,1,1}+ 24 s_{3,2,2,2}+ 6 s_{3,3,1,1,1}+ 30 s_{3,3,2,1}+ 12 s_{3, 3, 3}+ 6 s_{4,2,1,1,1}+ 60 s_{4,2,2,1}+ 42 s_{4,3,1,1}+ 68 s_{4,3,2}+ 30 s_{4,4,1}+ 36 s_{5,2,1,1}+ 85 s_{5,2,2}+ 96 s_{5,3,1}+ 36 s_{5,4}+ 66 s_{6,2,1}+ 72 s_{6,3}+ 36 s_{7,2} |
| Remarks | Source: R. Rimanyi: unpublished |