Thom polynomials and Schur functions: towards the singularities $A_i(-)$
| dc.creator | Pragacz, Piotr | |
| dc.date | 2008-10-14 | |
| dc.date.accessioned | 2026-07-07T10:09:56Z | |
| dc.date.available | 2026-07-07T10:09:56Z | |
| dc.description | We develop algebro-combinatorial tools for computing the Thom polynomials for the Morin singularities $A_i(-)$ ($i\ge 0$). The main tool is the function $F^{(i)}_r$ defined as a combination of Schur functions with certain numerical specializations of Schur polynomials as their coefficients. We show that the Thom polynomial ${\cal T}^{A_i}$ for the singularity $A_i$ (any $i$) associated with maps $({\bf C}^{\bullet},0) \to ({\bf C}^{\bullet+k},0)$, with any parameter $k\ge 0$, under the assumption that $Σ^j=\emptyset$ for all $j\ge 2$, is given by $F^{(i)}_{k+1}$. Equivalently, this says that "the 1-part" of ${\cal T}^{A_i}$ equals $F^{(i)}_{k+1}$. We investigate 2 examples when ${\cal T}^{A_i}$ apart from its 1-part consists also of the 2-part being a single Schur function with some multiplicity. Our computations combine the characterization of Thom polynomials via the "method of restriction equations" of Rimányi et al. with the techniques of Schur functions. | |
| dc.description | 16 pages; the paper appeared in Contemporary Math. vol.459, 2008 | |
| dc.identifier | https://arxiv.org/abs/0810.2441 | |
| dc.identifier | http://arxiv.org/abs/0810.2441 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171475 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 05E05, 14N10, 57R45 | |
| dc.title | Thom polynomials and Schur functions: towards the singularities $A_i(-)$ | |
| dc.type | text |