Abstract
We prove a formula for Thom polynomials of $A_d$ singularities in any codimension. We use a combination of the test-curve model of Porteous, and the localization methods in equivariant cohomology. Our formulas are independent of the codimension, and are computationally effective up to $d=6$.
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AUTHOR={Arnold, V. I. and Goryunov, V. V. and Lyashko, O. V. and Vasilliev, V. A.},
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@book {newstead, MRKEY = {0546290},
AUTHOR = {Newstead, P. E.},
TITLE = {Introduction to Moduli Problems and Orbit Spaces},
SERIES = {Tata Inst. Fund. Res. Lect. Math. Phys.},
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@inproceedings {forporteous, MRKEY = {0293646},
AUTHOR = {Porteous, Ian R.},
TITLE = {Simple singularities of maps},
BOOKTITLE = {Proceedings of {L}iverpool {S}ingularities {S}ymposium, {I} (1969/70)},
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ZBLNUMBER = {0221.57016},
DOI = {10.1007/BFb0066829},
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@incollection {por, MRKEY = {0713263},
AUTHOR = {Porteous, Ian R.},
TITLE = {Probing singularities},
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VENUE={{A}rcata, {C}alif., 1981},
SERIES = {Proc. Sympos. Pure Math.},
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YERA={2005},
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TITLE = {Le calcul des classes duales aux singularites de {B}oardman d'ordre 2},
JOURNAL = {C. R. Acad. Sci. Paris Sér. A-B},
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YEAR = {1970},
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AUTHOR = {Ronga, Felice},
TITLE = {A new look at {F}aà de {B}runo's formula for higher derivatives of composite functions and the expression of some intrinsic derivatives},
BOOKTITLE = {Singularities, {P}art 2},
VENUE={{A}rcata, {C}alif., 1981},
SERIES = {Proc. Sympos. Pure Math.},
VOLUME = {40},
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MRCLASS = {53.0X},
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@article {voj, MRKEY = {1072817},
AUTHOR = {Vergne, Mich{è}le},
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JOURNAL = {Ann. Sci. École Norm. Sup.},
FJOURNAL = {Annales Scientifiques de l'École Normale Supérieure. Quatrième Série},
VOLUME = {23},
YEAR = {1990},
NUMBER = {4},
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MRNUMBER = {1072817},
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}
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