Tjurina and Milnor numbers of matrix singularities
| dc.creator | Goryunov, Victor | |
| dc.creator | Mond, David | |
| dc.date | 2003-07-02 | |
| dc.date | 2003-07-11 | |
| dc.date.accessioned | 2026-07-07T04:59:21Z | |
| dc.date.available | 2026-07-07T04:59:21Z | |
| dc.description | In order to understand the deformations of determinants and Pfaffians resulting from deformations of matrices, we study the deformation theory of composites $f\circ F$, with isolated singularities, where $f:Y\to\C$ has Cohen-Macaulay singular locus and $F:X\to Y$. We identify the corresponding $T^1(F)$ as (something like) the cohomology of a derived functor, and construct a canonical long exact sequence from which it follows that $$τ=μ(f\circ F)-β_0+β_1,$$ where $τ$ is the length of $T^1(F)$ and $β_i$ is the length of $Tor_i(Ø_Y/J_f,Ø_X)$. This explains numerical coincidences observed in lists of simple matrix singularities due to Bruce, Tari, Goryunov, Zakalyukin and Haslinger. | |
| dc.description | LaTeX file; 23 pages; minor corrections | |
| dc.identifier | https://arxiv.org/abs/math/0307025 | |
| dc.identifier | http://arxiv.org/abs/math/0307025 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67951 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.subject | 14B05; 32S20 | |
| dc.title | Tjurina and Milnor numbers of matrix singularities | |
| dc.type | text |