Tjurina and Milnor numbers of matrix singularities

• Autores: V. Goryunov, David Mond
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 72, Nº 1, 2005, págs. 205-224
• Idioma: inglés
• DOI: 10.1112/s0024610705006575
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• Resumen

  • To gain understanding of the deformations of determinants and Pfaffians resulting from deformations of matrices, the deformation theory of composites with isolated singularities is studied, where is a function with (possibly non-isolated) singularity and is a map into the domain of , and only is deformed. The corresponding is identified as (something like) the cohomology of a derived functor, and a canonical long exact sequence is constructed from which it follows that , where is the length of and is the length of . This explains numerical coincidences observed in lists of simple matrix singularities due to Bruce, Tari, Goryunov, Zakalyukin and Haslinger. When has Cohen-Macaulay singular locus (for example when is the determinant function), relations between and the rank of the vanishing homology of the zero locus of are obtained.